Carboplatin, Paclitaxel and Gemcitabine Hydrochloride With or Without Bevacizumab After Surgery in Treating Patients With Recurrent Ovarian, Epithelial, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Patients enrolled after August 28, 2011 must be candidates for cytoreductive surgery and consent to have their surgical treatment determined by randomization * Patients must have histologic diagnosis of epithelial ovarian carcinoma, peritoneal primary or fallopian tube carcinoma, which is now recurrent * 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.) * Patients must have had a complete response to front-line platinum-taxane therapy (at least three cycles) * A complete response to front-line chemotherapy must include: negative physical exam, negative pelvic exam and normalization of CA125, if elevated at baseline; although not required, any radiographic assessment of disease status (e.g. CT, magnetic resonance imaging \[MRI\], positron emission tomography \[PET\]/CT, etc) obtained following the completion of primary therapy should be considered negative for disease * All patients must have also had a treatment-free interval without clinical evidence of progressive disease of at least 6 months from completion of front-line chemotherapy (both platinum and taxane); front-line therapy may have included a biologic agent (i.e. bevacizumab) * Front-line treatment may include maintenance therapy following complete clinical or pathological response; however, maintenance cytotoxic chemotherapy must be discontinued for a minimum of 6 months prior to documentation of recurrent disease; patients receiving maintenance biological therapy or hormonal therapy are ELIGIBLE provided their recurrence is documented more than 6 months from primary cytotoxic chemotherapy completion (includes maintenance chemotherapy) AND a minimum 4 weeks has elapsed since their last infusion of biological therapy * Patients must have clinically evident recurrent disease for the purpose of this study * Measurable disease (Response Evaluation Criteria in Solid Tumors \[RECIST\]) is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be more than or equal to 20 mm when measured by conventional techniques, MRI or CT, or more than or equal to 10 mm when measured by spiral CT * Absolute neutrophil count (ANC) greater than or equal to 1,500/mm\^3, equivalent to Common Toxicity Criteria for Adverse Events version (v)4.0 (CTCAE) grade 1 * Platelets greater than or equal to 100,000/mm\^3 (CTCAE grade 0-1) * Creatinine (non-isotope dilution mass spectrometry \[IDMS\]) =\< 1.5 x institutional upper limit normal (ULN), CTCAE grade 1 * Total bilirubin =\< 1.5 ULN (CTCAE grade 1) * Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) =\< 2.5 times the upper limit of normal in the absence of liver metastasis; SGOT/AST \< 5.0 times ULN in the presence of liver metastasis * Alkaline phosphatase =\< 2.5 times the upper limit of normal in the absence of liver metastasis; alkaline phosphatase \< 5.0 times ULN in the presence of liver metastasis * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients must have a urine protein-to-creatinine ratio (UPCR) \< 1.0 mg/dL * This eligibility criterion does not apply to patients enrolled after August 28, 2011; patients who are not candidates for surgical cytoreduction are eligible for the chemotherapy randomization; patients are not considered candidates for surgical cytoreduction if complete cytoreduction in the estimation of the investigator is impossible or a medical infirmity precludes exploration and debulking * Patients must have met the pre-entry requirements as specified * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients must have a Gynecologic Oncology Group (GOG) performance status of 0, 1, or 2 Exclusion Criteria: * Patients who have received more than one previous regimen of chemotherapy (maintenance is not considered a second regimen) * Patients receiving concurrent immunotherapy, or radiotherapy * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis are excluded * Patients whom have already undergone secondary cytoreduction for recurrent disease are excluded * Patients with a prior histologic diagnosis of borderline, low malignant potential (grade 0) epithelial carcinoma that was surgically resected and who subsequently developed an unrelated, new invasive epithelial ovarian or peritoneal primary cancer are eligible provided that they meet the criteria listed above * Patients who require parenteral hydration or nutrition and have evidence of partial bowel obstruction or perforation * Patients who have received prior chemotherapy for any abdominal or pelvic tumor (other than ovarian, fallopian tube, and primary peritoneal) are excluded * 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 International Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions * Patients with uncontrolled infection * Patients with concurrent severe medical problems unrelated to the malignancy that would significantly limit full compliance with the study or expose the patient to extreme risk or decreased life expectancy * Patients with \>= grade 2 peripheral neuropathy * Patients with a history of allergic reactions to carboplatin and/or paclitaxel or chemically similar compounds; patients with allergic (hypersensitivity) reactions to these chemotherapeutic agents are NOT excluded IF they were successfully retreated following a desensitization program or protocol * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * Patients of childbearing potential, not practicing adequate contraception, patients who are pregnant or patients who are nursing are not eligible for this trial; to date, no fetal studies in animal or humans have been performed; the possibility of harm to a fetus is likely; bevacizumab specifically inhibits VEGF, which is responsible for the formation of new blood vessels during development, and antibodies can cross the placenta; therefore, bevacizumab should not be administered to pregnant women; in addition, there are unknown immediate and long-term consequences of chemotherapy administration to these women; in addition, surgical exploration as mandated by randomization during pregnancy may cause imminent mortal consequences; further, it is not known whether bevacizumab is excreted in human milk; because many drugs are excreted in human milk, bevacizumab should not be administered to nursing women; subjects will be apprised of the large potential risk to a developing fetus * Patients with other invasive malignancies, with the exception of non-melanoma skin cancer, who had (or have) any evidence of the other cancer present within the last 5 years or whose previous cancer treatment contraindicates this protocol therapy * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with active bleeding or pathologic conditions that carry high risk of bleeding such as a known bleeding disorder, coagulopathy, or tumor involving major vessels * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with a 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 a history of stroke within 5 years of the first date of treatment on this study * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with clinically significant cardiovascular disease; this includes: * Patients with significant cardiac conduction abnormalities, i.e. PR interval \> 0.24 seconds (sec) or 2nd or 3rd degree atrioventricular (AV) block * Uncontrolled hypertension, defined as systolic \> 150 mm Hg or diastolic \> 90 mm Hg * Myocardial infarction, cardiac arrhythmia 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 * Grade II or greater peripheral vascular disease (exception: episodes of ischemia \< 24 hours \[hrs\] in duration, that are managed non-surgically and without permanent deficit) * History of cerebrovascular attack (CVA) within six months * This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients who have had a major surgical procedure, open biopsy, dental extractions or other dental surgery/procedure that results in an open wound, or significant traumatic injury within 28 days prior to the first date of treatment on this study, or anticipation of need for major surgical procedure during the course of the study; patients with placement of vascular access device or core biopsy within 7 days prior to the first date of treatment on this study * Patients undergoing pre-treatment secondary cytoreduction will undergo therapy with bevacizumab on cycle #2 * Patients undergoing pre-treatment surgery for purposes other than cytoreduction may also participate provided they meet eligibility; patients randomized to arms containing bevacizumab must wait a minimum of 28 days since that procedure to begin protocol treatment; patients who undergo an uncomplicated port placement must wait a minimum of 7 days to begin protocol treatment