Inclusion Criteria:  Signed written 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. Female patients ≥ 18 years with histologically confirmed primary advanced invasive high grade epithelial ovarian cancer, peritoneal cancer, or fallopian tube cancer FIGO III/IV (except FIGO stage IIIA2 without nodal involvement) according to recent FIGO classification (= FIGO stage IIIB - IV according to FIGO 2009 classification). All patients must have had either upfront primary debulking surgery OR plan to undergo chemotherapy with interval debulking surgery. Patients must have available tumor samples to be sent to central laboratory as formalin-fixed, paraffin-embedded (FFPE) sample for determination of BRCA status prior to randomization for stratification. Patients must be able to commence systemic therapy within 8 weeks of cytoreductive surgery. Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1. Estimated life expectancy > 3 months.  Adequate bone marrow function (within 28 days prior to day 1, cycle 1)  Absolute Neutrophil Count (ANC) ≥ 1.5 x 10^9/L Platelets (PLT) ≥ 100 x 10^9/L Hemoglobin (Hb) ≥ 9 g/dL (can be post-transfusion)  Adequate coagulation parameters (within 28 days prior to day 1, cycle 1)  Patients not receiving anticoagulant medication who have an International Normalized Ratio (INR) ≤ 1.5 and an Activated ProThrombin Time (aPTT) ≤ 1.5 x institutional upper limit of normal (ULN). The use of full-dose oral or parenteral anticoagulants is permitted as long as the INR or aPTT is within therapeutic limits (according to institution medical standard) and the patient has been on a stable dose of anticoagulants for at least two weeks at the time of day 1, cycle 1.  Adequate liver and kidney function (within 28 days prior to day 1, cycle 1)  Total bilirubin ≤ 1.5 x ULN (≤ 2.0 x ULN in patients with known Gilbert's syndrome) OR direct bilirubin ≤ 1.0 x ULN. Aspartate aminotransferase / Serum Glutamic Oxaloacetic Transaminase (ASAT/SGOT) and Alanine aminotransferase / Serum Glutamic Pyruvate Transaminase (ALAT/SGPT) ≤ 2.5 x ULN, unless liver metastases are present, in case of liver metastases values must be ≤ 5 x ULN. Urine dipstick for proteinuria < 2+. If urine dipstick is ≥ 2+, 24 hour urine must demonstrate ≤ 1 g of protein in 24 hours. Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or calculated creatinine clearance ≥ 30 mL/min using the Cockcroft-Gault equation. Patients must have normal blood pressure (BP) or adequately treated and controlled BP, with a systolic BP of ≤ 140 mmHg and diastolic BP of ≤ 90 mmHg for eligibility. Patients must have a BP of ≤ 140/90 mmHg taken in the clinic setting by a medical professional within 4 weeks prior to day 1, cycle 1. Negative urine or serum pregnancy test within 7 days prior to day 1, cycle 1 in women of childbearing potential (WOCBP), confirmed prior to treatment on day 1.  For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a highly effective contraceptive method with a failure rate of < 1% per year during the treatment period and for at least 6 months after administration of the last dose of medication.  A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries, fallopian tubes, and/or uterus).  Examples of contraceptive methods with a failure rate of < 1% per year include but are not limited to bilateral tubal ligation and/or occlusion, male sterilization, and intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical study 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.  Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures, that include the completion of patient-reported outcomes questionnaires.  Exclusion Criteria:  Non-epithelial tumor origin of the ovary. Ovarian tumors of low malignant potential (e.g. borderline tumors) and low grade tumors. Planned intraperitoneal cytotoxic chemotherapy. Malignancies other than ovarian cancer within 5 years prior to randomization, with the exception of those with a negligible risk of metastasis or death (e.g., 5-year OS rate > 90%) and treated with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, ductal carcinoma in situ of the breast, or stage I p53 wild type endometrial cancer). Prior systemic treatment for ovarian cancer. Prior treatment with Poly adenosine diphosphate ribose polymerase (PARP) inhibitor. Administration of other simultaneous chemotherapy drugs, any other anticancer therapy or anti-neoplastic hormonal therapy, or simultaneous radiotherapy during the trial treatment period (hormonal replacement therapy is permitted). Prior randomization in this trial. Major surgery within 1 week of starting study treatment or patient who has not completely recovered from the effects of any major surgery. Core biopsy or other minor surgical procedure within 7 days prior to day 1, cycle 1 is permitted. History or clinical suspicion of brain metastases or spinal cord compression. CT/MRI of the brain is mandatory (within 4 weeks prior to day 1, cycle 1) in case of suspected brain metastases. Spinal MRI is mandatory (within 4 weeks prior to day 1, cycle 1) in case of suspected spinal cord compression. Significant traumatic injury during 4 weeks preceding the potential first dose of bevacizumab. Previous Cerebro-Vascular Accident (CVA), Transient Ischemic Attack (TIA) or Sub-Arachnoids Hemorrhage (SAH) within 6 months prior to day 1, cycle 1. History or evidence of thrombotic or hemorrhagic disorders within 3 months prior to day 1, cycle 1. History or evidence upon neurological examination of central nervous system (CNS) disease, unless adequately treated with standard medical therapy e.g. uncontrolled seizures. Fertile woman of childbearing potential not willing to use adequate contraception (oral contraceptives, intrauterine device or barrier method of contraception in conjunction with spermicidal jelly or surgically sterile) for the study duration and at least 6 months afterwards. Pregnant or lactating women. Treatment with any other investigational agent, or participation in another clinical trial testing a drug within the past 4 weeks before start of therapy or concomitantly with this trial. Known hypersensitivity to bevacizumab and its excipients, Chinese hamster ovary cell products or other recombinant human or humanized antibodies. Known hypersensitivity to niraparib, paclitaxel and carboplatin and its components or excipients. Non-healing wound, active ulcer or bone fracture. Patients with granulating incisions healing by secondary intention with no evidence of facial dehiscence or infection are eligible but require 3-weekly wound examinations.  Clinically significant cardiovascular disease, including  Myocardial infarction or unstable angina within 6 months of day 1, cycle 1 New York Heart Association (NYHA) Grade 2 Congestive Heart Failure (CHF), Poorly controlled cardiac arrhythmia despite medication (patients with rate-controlled atrial fibrillation are eligible) Grade ≥ 3 peripheral vascular disease (i.e. symptomatic and interfering with activity of daily living (ADL) requiring repair or revision) Pre-existing sensory or motor neuropathy ≥ Grade 2. Any prior history of hypertensive crisis (CTCAE grade 4) or hypertensive encephalopathy. Patients with a history of or current Nephrotic syndrome. Bowel obstruction (including subocclusive disease). History of abdominal fistula or gastrointestinal perforation or active gastrointestinal bleeding or anastomotic insufficiency within 6 months of day 1, cycle 1. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of niraparib. Evidence of any other disease, metabolic dysfunction, physical examination finding or laboratory finding giving reasonable suspicion of a disease or condition that contra-indicates the use of an investigational drug or puts the patient at high risk for treatment-related complications. Any known history or current diagnosis of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). Previous allogeneic bone marrow transplant or previous solid organ transplantation. Current or recent (within 10 days prior to day 1, cycle 1) chronic use of aspirin > 325 mg/day. Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. This includes also any psychiatric disorder that prohibits obtaining informed consent. Patient has known active hepatitis B or hepatitis C. Patient has a history of Posterior Reversible Encephalopathy Syndrome (PRES).