Carboplatin, Paclitaxel, Bevacizumab, and Veliparib in Treating Patients With Newly Diagnosed Stage II-IV Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients with a histologic diagnosis of epithelial ovarian, fallopian tube, or primary peritoneal carcinoma, or carcinosarcoma stage II, III, or IV with either optimal (=\< 1 cm residual disease) or suboptimal residual disease * All patients must have a procedure for determining diagnosis of epithelial ovarian, fallopian tube, primary peritoneal, or carcinosarcoma with appropriate tissue for histologic evaluation * Patients with the following histologic cell types are eligible: * Serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial adenocarcinoma, transitional cell carcinoma, malignant Brenner's tumor, adenocarcinoma not otherwise specified (N.O.S.) or carcinosarcoma * Absolute neutrophil count (ANC) greater than or equal to 1,500/mm\^3, equivalent to CTEP Common Terminology Criteria for Adverse Events (CTCAE) version 4.0, grade 1; this ANC cannot have been induced or supported by granulocyte colony stimulating factors * Platelets greater than or equal to 100,000/mm\^3 * Regimens I and II: Creatinine =\< 1.5 x institutional upper limit normal (ULN), CTCAE grade 1 * Regimen III: Creatinine no greater than the institutional upper limits of normal * Bilirubin less than or equal to 1.5 x ULN (CTEP CTCAE version 4.0, grade 1) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) less than or equal to 3 x ULN (CTEP CTCAE version 4.0, grade 1) * Alkaline phosphatase less than or equal to 2.5 x ULN (CTEP CTCAE version 4.0, grade 1) * Albumin greater than or equal to 3.0 g/dL * Neuropathy (sensory and motor) less than or equal to CTEP CTCAE version 4.0, grade 1 * Prothrombin time (PT) such that international normalized ratio (INR) is =\< 1.5 x ULN (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) and a partial thromboplastin time (PTT) \< 1.5 x ULN * Patients must have a Gynecologic Oncology Group (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 who have met the pre-entry requirements specified * Patients must have signed an approved informed consent and authorization permitting release of personal health information 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 * NOTE: 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 with synchronous primary endometrial cancer or a past history of endometrial cancer, unless all of the following conditions are met: * Stage not greater than IB * No more than superficial myometrial invasion * No 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 a history of other invasive malignancies, with the exception of non-melanoma skin cancer and other specific malignancies as noted, are excluded if there is any evidence of other malignancy being present within the last five years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy * 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 within the last five years 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 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 or history of seizures, and/or any CNS metastases are ineligible * Patients with 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 are ineligible * 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) class II or higher congestive heart failure * Serious cardiac arrhythmia requiring medication * CTEP CTCAE version 4.0, grade 2 or higher peripheral ischemia (brief \[\< 24 hours (hrs)\] episode of ischemia managed non-surgically and without permanent deficit) * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * Patients with clinically significant proteinuria (urine protein creatinine ratio greater or equal to 1.0) * Patients with invasive procedures or anticipation of invasive procedures within the following timeframes as defined below: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to the first date of bevacizumab therapy (cycle 2) * Major surgical procedure anticipated during the course of the study * Core biopsy within 7 days prior to the first date of bevacizumab therapy (cycle 2) * Patients who are pregnant or nursing * Patients with clinical symptoms or signs of gastrointestinal obstruction and who require parenteral hydration or nutrition * Patients with GOG performance status of 3 or 4