Paclitaxel and Bevacizumab With or Without Emactuzumab in Treating Patients With Platinum-Resistant Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Signed informed consent obtained prior to initiation of any study-specific procedures and treatment as confirmation of the patient's awareness and willingness to comply with the study requirements (inclusive of 2 biopsies, one at baseline and if they qualify, one pre-randomization for part 2B) * Women 18 years of age or older * Histologically confirmed and documented disease to include: adenocarcinoma NOS (not otherwise specified), clear cell adenocarcinoma, endometrioid adenocarcinoma, malignant Brenner's tumor, mixed epithelial carcinoma, mucinous adenocarcinoma, serous adenocarcinoma, transitional cell carcinoma, and undifferentiated carcinoma * Patients must have platinum-resistant disease, (defined as progression within \< 6 months from completion of a minimum of 4 platinum therapy cycles (+ 7 days); the date should be calculated from the last administered dose of platinum therapy) * Patients must have disease that is measurable according to RECIST 1.1 or assessable according to the GCIG CA-125 criteria and require chemotherapy treatment; part 1: patients must have one or more measurable target lesion; part 2: patients must have two or more measurable target lesions; measurable disease is defined at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each 'target' lesion must be \>= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \>= 10 mm when measured by spiral CT * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Newly obtained core or excisional biopsy of a tumor lesion for part 2A and if they qualify, one pre-randomization biopsy for part 2B * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>=9 g/dL or \>= 5.6 mmol/L * Creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional upper limit of normal (ULN) * Total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGOT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases * International normalized ratio (INR)/prothrombin time (PT) =\< 1.5 X ULN (unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time \[PTT\] is within therapeutic range of intended use of anticoagulants) * PTT =\< 1.5 X ULN (unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants) * Life expectancy of \>= 12 weeks Exclusion Criteria: * Patients who have disease progression prior to completion of intended frontline therapy, including patients demonstrating disease progression after interval cytoreduction * Non-epithelial, including malignant mixed Mullerian tumors * Ovarian tumors with low malignant potential (i.e. borderline tumors) * For part 2 patients only: History of other clinically active malignancy within 5 years of enrollment, except for tumors with a negligible risk for metastasis or death, such as adequately controlled basal-cell carcinoma or squamous-cell carcinoma of the skin or carcinoma in situ of the cervix or breast, or early stage endometrial cancer (stage IA/B, grade 1 or 2, endometrioid histology) * Previous treatment with \> 2 anticancer regimens for ovarian cancer * Any approved anti-cancer therapy, including chemotherapy or hormonal therapy, within 3 weeks prior to initiation of study treatment, with the following exceptions: hormone-replacement therapy or oral contraceptives; tyrosine kinase inhibitors (TKIs) that have been discontinued \> 7 days prior to cycle 1, day 1; screening scans must be obtained after discontinuation of prior TKIs * Any prior radiotherapy to the pelvis or abdomen * Surgical procedure (including open biopsy, surgical resection, wound revision, or any other major surgery involving entry into a body cavity) or significant traumatic injury within 28 days prior to study enrollment, or anticipation of need for major surgical procedure during the course of the study; minor surgical procedures including placement of a vascular access device, within 2 days of the first study treatment * Previous exposure to murine CA-125 antibody (only applicable to those patients with non-measurable disease by RECIST) * Current or recent (within 10 days prior to the first study drug dose) chronic daily treatment with aspirin (\> 325 mg/day) * Current or recent treatment with another investigational drug within 30 days of first study treatment dosing or earlier participation in this study * Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF agents within 2 weeks prior to cycle 1, day 1; patients who have received acute and/or lowrolment, or anticipation of need for major surgical, a one-time dose of dexamethasone for nausea or chronic use of =\< 10 mg/day of prednisone or dose-equivalent corticosteroid) may be enrolled in the study after discussion with and approval by the medical monitor; the use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) is allowed; prior corticosteroids as anti-cancer therapy within a minimum of 14 days of first receipt of study drug * Received therapeutic oral or IV antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible * Patients with urine dipstick for proteinuria \> 2+; patients with \>= 2+ proteinuria on baseline dipstick analysis should undergo a 24-hour urine collection and must demonstrate =\< 1 g of protein in the 24-hour urine; alternatively, proteinuria testing can be performed according to local standards * Patients with known auto-immune disease * Patients with known history of human immunodeficiency virus (HIV), hepatitis B virus (HBV) and hepatitis C virus (HCV) infection * Patient has received an organ transplant * Patient has a history of hematological malignancy within the last 5 years prior to study entry; prior allogeneic bone marrow transplantation or prior solid organ transplantation * Patient has a history of hematological malignancy within the last 5 years prior to study entry * History of or active autoimmune disease including, but not limited to, systemic lupus erythematous, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, and vasculitis or glomerulonephritis; patients with autoimmune thyroid disease on a stable thyroid replacement regimen; controlled vitiligo, eczema, psoriasis, or seborrheic dermatitis with only dermatologic manifestations; or controlled type I diabetes on a stable insulin regimen may be eligible for the study with approval by the medical monitor * History or evidence upon physical/neurological examination of central nervous system (CNS) disease unrelated to cancer, unless adequately treated with standard medical therapy (e.g. uncontrolled seizures) * Symptomatic CNS metastasis * Pre-existing peripheral neuropathy \>= Common Terminology Criteria (CTC) grade 2 for those patients who received prior paclitaxel * Spinal cord compression not definitively treated with surgery and/or radiation or previously diagnosed and treated spinal cord compression without evidence that disease has been clinically stable for \>= 2 weeks prior to screening * Increased corrected QT (QTc) interval (QTc \> 470 ms), patients with baseline resting bradycardia \< 45 beats per minute (bpm), or baseline resting tachycardia \> 100 bpm * Family history of long QT syndrome or other risk factors for torsades de pointes, and/or the use of concomitant medications that prolong the QT/QTc interval * Signs or symptoms of serious active infection requiring oral or i.v. antibiotics within 2 weeks prior to cycle 1 day 1 and/or hospitalization at study entry including, but not limited to, hospitalization for complications of infection, bacteremia, active tuberculosis or severe pneumonia * Pregnant or lactating females; serum pregnancy test to be assessed within 7 days prior to study treatment start, or within 14 days (with a confirmatory urine pregnancy test within 7 days prior to study treatment start) * For women who are not postmenopausal (\< 12 months of non therapy-induced amenorrhea, with no identified cause other than menopause) and have not undergone surgical sterilization (removal of ovaries and/or uterus): agreement to remain abstinent (refrain from heterosexual intercourse) or use two adequate non hormonal methods of contraception, including at least one method with a failure rate of \< 1% per year, during the treatment period and for at least 4 months after the last dose of study drug * Examples of non-hormonal contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, established, proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices; the reliability of sexual abstinence needs to be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient; periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception * History or evidence of thrombotic or hemorrhagic disorders; including cerebrovascular accident (CVA)/stroke or transient ischemic attack (TIA) or sub-arachnoid hemorrhage within =\< 6 months prior to the first study treatment * Uncontrolled hypertension (sustained systolic \> 150 mmHg and/or diastolic \> 100 mmHg despite antihypertensive therapy) or clinically significant (i.e. active) cardiovascular disease, including: myocardial infarction or unstable angina within =\< 6 months prior to the first study treatment; New York Heart Association (NYHA) grade II or greater congestive heart failure (CHF); serious cardiac arrhythmia requiring medication (with the exception of atrial fibrillation or paroxysmal supraventricular tachycardia); significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior of study enrollment; prior history of hypertensive crisis or hypertensive encephalopathy * History of bowel obstruction, including sub-occlusive disease, related to the underlying disease and history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess; evidence of recto-sigmoid involvement by pelvic examination or bowel involvement on CT scan or clinical symptoms of bowel obstruction * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * History of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) within 1 month of study enrollment for any tumor type * Non-healing wound, ulcer or bone fracture * Known hypersensitivity to any of the study drugs or excipients * Evidence of any other medical conditions (such as psychiatric illness, peptic ulcer, etc.), physical examination or laboratory findings that may interfere with the planned treatment, affect patient compliance or place the patient at high risk from treatment-related complications