The goal of this clinical research study is to learn if Avastin (bevacizumab) can help to control ovarian, fallopian, or primary peritoneal cancer that has been found during second-look surgery.

Study Drug Administration:

If you are found to be eligible to take part in the study, you will receive bevacizumab by vein over about 30 minutes on Day 1 of every 21-day study cycle.

Study Visits:

Your first study visit will be about 5-7 weeks after your second-look surgery so that you have time to recover. The study doctor will tell you when you will start having study visits.

During all cycles:

• You will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine testing. If you can become pregnant and the doctor thinks it is needed, part of this routine blood sample may be used for a pregnancy test.

During Cycle 3 and then every 3 cycles after that (Cycles 6, 9, 12, and so on), you will have an MRI or CT scan.

Length of Treatment:

You may continue to receive bevacizumab for as long as the study doctor thinks it is in your best interest. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

Your participation on the study will be over after the end-of-treatment visit.

End-of-Treatment Visit:

Within about 7 days after your last dose of bevacizumab:

• You will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine testing. If you can become pregnant, part of this sample will be used for a pregnancy test.

This is an investigational study. Bevacizumab is FDA approved and commercially available for the treatment of several types of cancer, including ovarian cancer. However, it is considered investigational to use bevacizumab as treatment for cancer found during second-look surgery.

The study doctor will explain how the study drug is designed to work.

Up to 35 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Signed written Informed Consent (in participant's preferred language or short form, per SOP04).
2. Age>/= 18 years of age or older.
3. Histologically confirmed Stage III-IV high-grade epithelial non-mucinous ovarian, fallopian tube, or primary peritoneal cancers.
4. Have received standard of care frontline surgical and chemotherapy treatment (at least six cycles of platinum and taxane therapy). Patients who received neoadjuvant therapy are included.
5. Have undergone a second-look surgery by an MD Anderson Gynecologic Oncology faculty after having achieved a complete clinical response to frontline surgery and adjuvant chemotherapy as evidenced by (a) normal physical exam, (b) normal CT or positron emission computed tomography (PET)-CT of abdomen and pelvis or other equivalent imaging, and (c) normalization of CA125 (<35 U/mL).
6. Histologically confirmed residual ovarian cancer at time of second-look surgery. Patients with cytological evidence of malignant cells in washings obtained as part of the second look procedure are eligible even if biopsies are negative.
7. Be willing to allow use of archival tissue from second-look surgery and primary surgery or biopsy for use in this study.
8. Have a performance status of 0, 1, or 2 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale at the time of screening.
9. Have adequate organ function as determined by the following laboratory values: a) absolute neutrophil count (ANC) >/= 1,000 /mcL; b) Platelets >/= 100,000/mcL; (c) Hgb >/= 8 g/dL; (d) Creatinine Clearance >/= 40 mL/min (measured or calculated per local practice); (e) Total Bilirubin </= 1.5 × upper limit of normal (ULN) or </= 3 × ULN in the case of suspected/documented Gilbert's Syndrome; and (f) AST (SGOT) and ALT (SGPT) </= 2.5 X ULN.
10. Have adequately recovered from second look surgery to be able to start bevacizumab within 7 weeks of this procedure.
11. Negative serum pregnancy within 72 hours prior to receiving the first dose of study medication (unless surgically sterile or postmenopausal for greater than one year).
12. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 1 year.

Exclusion Criteria:

1. Uncontrolled hypertension as defined by SBP>150 or DBP>90 on at least two separate occasions documented in the medical record. Patients would be eligible if blood pressure is controlled with appropriate anti-hypertensive therapy. Rescreening after this therapy has been instituted is allowed.
2. Histology showing mucinous or low-grade epithelial ovarian carcinoma.
3. Documented germline or somatic BRCA mutations and/or HRD positivity.
4. Planned use of maintenance or consolidative therapy.
5. History of known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the Study.
6. History of arterial thrombosis. Patients with history of DVT are eligible as long as they have received or are receiving appropriate anticoagulation therapy.
7. History of gastrointestinal or urinary fistulae, non-healed or chronic wound, or other conditions that, in the investigator's view, would contraindicate or significantly increase the risks of bevacizumab therapy.
8. History of known hemoptysis, gastrointestinal or intracerebral hemorrhage.
9. Patient that is not able to understand or to comply with the study instructions and requirements, or has a history of non-compliance to the medical regimen.
10. Concurrent or planned use of any other anti-cancer systemic chemotherapy, biological therapy (including hormonal or immune therapy), radiation therapy, or live cancer vaccines.
11. Prior use of bevacizumab or a biosimilar in the frontline treatment setting.