Carboplatin and Paclitaxel With or Without Bevacizumab in Treating Patients With Stage III or Stage IV Ovarian Epithelial, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Patients with a histologic diagnosis of epithelial ovarian cancer, peritoneal primary carcinoma or fallopian tube cancer; International Federation of Gynecology and Obstetrics (FIGO) stage III with any gross (macroscopic or palpable) residual disease or FIGO stage IV, defined surgically at the completion of initial abdominal surgery and with appropriate tissue available for histologic evaluation; the minimum surgery required was an abdominal surgery providing tissue for histologic evaluation and establishing and documenting the primary site and stage, as well as a maximal effort at tumor debulking; if additional surgery was performed, it should have been in accordance with appropriate surgery for ovarian or peritoneal carcinoma described in the Gynecologic Oncology Group (GOG) Surgical Procedures Manual; however, the surgeon is not required to have performed all of the items contained in this section of the GOG Surgical Procedures Manual; those patients with stage III cancer in which the largest maximal diameter of any residual tumor implant at the completion of this initial surgery is no greater than 1 cm will be defined as "optimal;" all others will be defined as "suboptimal;" measurable disease on post-operative imaging studies is not required for eligibility * Patients with the following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's Tumor, or adenocarcinoma not otherwise specified (N.O.S.); however, the histologic features of the tumor must be compatible with a primary Müllerian epithelial adenocarcinoma; if doubt exists, it is recommended that the investigator should have the slides reviewed by an independent pathologist or, if necessary, the Pathology Co-Chair, prior to entry; patients may have co-existing fallopian tube carcinoma in-situ so long as the primary origin of invasive tumor is ovarian, peritoneal or fallopian tube * Absolute neutrophil count (ANC) greater than or equal to 1,500/µl equivalent to Common Toxicity Criteria for Adverse Events version (v)3.0 (CTCAE) grade 1; this ANC cannot have been induced or supported by granulocyte colony stimulating factors * Platelets greater than or equal to 100,000/µl; (CTCAE grade 0-1) * Creatinine =\< 1.5 x institutional upper limit normal (ULN), CTCAE grade 1 * Bilirubin less than or equal to 1.5 x ULN (CTCAE grade 1) * Serum glutamic oxaloacetic transaminase (SGOT) and alkaline phosphatase less than or equal to 2.5 x ULN (CTCAE grade 1) * Neuropathy (sensory and motor) less than or equal to CTCAE grade 1 * Prothrombin time (PT) such that international normalized ratio (INR) is =\< 1.5 (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin for management of venous thrombosis including pulmonary thrombo-embolus) and a partial thromboplastin time (PTT) \< 1.2 times the upper limit of normal * Patients with a GOG Performance Status of 0, 1, or 2 * Patients must be entered between 1 and 12 weeks after initial surgery performed for the combined purpose of diagnosis, staging and cytoreduction * Patients with measurable and non-measurable disease are eligible; patients may or may not have cancer-related symptoms * Patients who have met the pre-entry requirements * An approved informed consent and authorization permitting release of personal health information must be signed by the patient or guardian * Patients in this trial may receive ovarian estrogen +/- progestin replacement therapy as indicated at the lowest effective dose(s) for control of menopausal symptoms at any time, but not progestins for management of anorexia while on protocol directed therapy or prior to disease progression Exclusion Criteria: * Patients with a current diagnosis of borderline epithelial ovarian tumor (formerly "tumors of low malignant potential") or recurrent invasive epithelial ovarian, primary peritoneal or fallopian tube cancer treated with surgery only (such as patients with stage Ia or Ib low grade epithelial ovarian or fallopian tube cancers) are not eligible; patients with a prior diagnosis of a borderline tumor that was surgically resected and who subsequently develop an unrelated, new invasive epithelial ovarian, peritoneal primary or fallopian tube cancer are eligible, provided that they have not received prior chemotherapy for any ovarian tumor * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis are excluded; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients who have received prior chemotherapy for any abdominal or pelvic tumor including neo-adjuvant chemotherapy for their ovarian, primary peritoneal or fallopian tube cancer are excluded; patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease * Patients who have received any targeted therapy (including but not limited to vaccines, antibodies, tyrosine kinase inhibitors) or hormonal therapy for management of their epithelial ovarian or peritoneal primary cancer * Patients with synchronous primary endometrial cancer, or a past history of primary endometrial cancer, are excluded, unless all of the following conditions are met: stage not greater than I-B; no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous, clear cell or other FIGO grade 3 lesions * With the exception of non-melanoma skin cancer and other specific malignancies as noted above, patients with other invasive malignancies who had (or have) any evidence of the other cancer present within the last five years or whose previous cancer treatment contraindicates this protocol therapy are excluded * Patients with acute hepatitis or active infection that requires parenteral antibiotics * Patients with serious non-healing wound, ulcer, or bone fracture; this includes history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days; patients with granulating incisions healing by secondary intention with no evidence of fascial dehiscence or infection are eligible but require weekly wound examinations * Patients with active bleeding or pathologic conditions that carry high risk of bleeding, such as known bleeding disorder, coagulopathy, or tumor involving major vessels * Patients with history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within six months of the first date of treatment on this study * Patients with clinically significant cardiovascular disease; this includes: * Uncontrolled hypertension, defined as systolic \> 150 mm Hg or diastolic \> 90 mm Hg * Myocardial infarction or unstable angina \< 6 months prior to registration * New York Heart Association (NYHA) grade II or greater congestive heart failure * Serious cardiac arrhythmia requiring medication; this does not include asymptomatic, atrial fibrillation with controlled ventricular rate * CTCAE grade 2 or greater peripheral vascular disease (at least brief (\< 24 hrs) episodes of ischemia managed non-surgically and without permanent deficit) * History of CVA within six months * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * Patients with clinically significant proteinuria; urine protein should be screened by urine protein-creatinine ratio (UPCR); the UPCR has been found to correlate directly with the amount of protein excreted in a 24 hour urine collection; specifically, a UPCR of 1.0 is equivalent to 1.0 gram of protein in a 24 hour urine collection; obtain at least 4 ml of a random urine sample in a sterile container (does not have to be a 24 hour urine); send sample to lab with request for urine protein and creatinine levels \[separate requests\]; the lab will measure protein concentration (mg/dL) and creatinine concentration (mg/dL); the UPCR is derived as follows: protein concentration (mg/dL)/creatinine (mg/dL); patients must have a UPCR \< 1.0 to allow participation in the study * Patients with or with anticipation of invasive procedures as defined below: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to the first date of bevacizumab/placebo therapy (cycle 2) * Major surgical procedure anticipated during the course of the study; this includes, but is not limited to abdominal surgery (laparotomy or laparoscopy) prior to disease progression, such as colostomy or enterostomy reversal, interval or secondary cytoreductive surgery, or second look surgery; please consult with the study chair prior to patient entry for any questions related to the classification of surgical procedures * Core biopsy, within 7 days prior to the first date of bevacizumab/placebo therapy (cycle 2) * Patients with GOG Performance Grade of 3 or 4 * Patients who are pregnant or nursing; bevacizumab should not be administered to nursing women; patients of childbearing potential must agree to use contraceptive measures during study therapy and for at least six months after completion of bevacizumab therapy * Patients who have received prior therapy with any anti-vascular endothelial growth factor (VEGF) drug, including bevacizumab * Patients with clinical symptoms or signs of gastrointestinal obstruction and who require parenteral hydration and/or nutrition * Patients with medical history or conditions not otherwise previously specified which in the opinion of the investigator should exclude participation in this study; the investigator should feel free to consult the study chair or study co-chairs for uncertainty in this regard