Matched Paired Pharmacodynamics and Feasibility Study of Durvalumab in Combination With Chemotherapy in Frontline Ovarian Cancer (N-Dur)

Inclusion Criteria: * Written informed consent and any locally-required authorization (e.g., Health Information Portability and Accountability Act \[HIPAA\] in the United States of America \[USA\], European Union \[EU\] Data Privacy Directive in the EU) obtained from the subject prior to performing any protocol-related procedures, including screening evaluations * Histology showing high-grade epithelial non-mucinous ovarian, primary peritoneal, or fallopian tube cancer * No prior treatment for primary advanced (stage III or IV) epithelial ovarian, primary peritoneal, or fallopian tube carcinoma such as irradiation, chemotherapy, hormonal therapy, immunotherapy, investigational therapy, surgery, and/or other concurrent agents or therapies * A disposition to neoadjuvant chemotherapy with planned interval tumor reductive surgery after 3 complete cycles of treatment * Planned chemotherapy with combination carboplatin and paclitaxel given intravenously * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 * Measurable disease is defined at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each target lesion must be \> 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \> 10 mm when measured by spiral CT * Patients with non-measurable but evaluable solid tumors may be deemed eligible contingent upon principal investigator (PI) review; a non-measurable but evaluable solid tumor is defined as either unidimensionally measurable lesions, masses with margins not clearly defined, or lesions with maximal perpendicular diameters \< 10 mm that can still be evaluated for the primary endpoint * Peripheral neuropathy grade 0 or 1 by National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.03 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy \>= 12 weeks * Hemoglobin (Hgb) \>= 9 g/dL * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (\> 1500 per mm\^3) * Platelet count \>= 100 x 10\^9/L (\> 100,000 per mm\^3) * Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate Transaminase (AST) and alanine transaminase (ALT) =\< 2.5 x institutional upper limit of normal (ULN) unless liver metastases are present, in which case it must be =\< 5 x ULN * Serum creatinine clearance (CL) \> 40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine * Subjects must either be of non-reproductive potential (i.e., post-menopausal by history: \>= 60 years old and no menses for \>= 1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test upon study entry * Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Pre-treatment tumor tissue available for research purposes; this tissue can be collected from preoperative laparoscopy, other diagnostic biopsy, or a research-specific biopsy; this pre-treatment tumor must be amenable to repeat tissue sampling after induction therapy * Signed informed consent on protocol LAB02-188 * For participation in the patient-reported outcomes and qualitative interviews, subjects must be fluent in English Exclusion Criteria: * Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site) * Previous enrollment in the present study * Prior treatment for ovarian, fallopian tube, or primary peritoneal cancer * Histology showing mucinous or low grade epithelial carcinoma * Participation in another clinical study with an investigational product during the last 4 weeks * Any previous treatment with a programmed cell death protein 1 (PD1) or programmed cell death ligand 1 (PD-L1) inhibitor, including durvalumab * History of another primary malignancy except for: malignancy treated with curative intent and with no known active disease \>= 5 years before the first dose of study drug and of low potential risk for recurrence; adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease; or adequately treated carcinoma in situ without evidence of disease e.g., cervical cancer in situ * Mean QT interval corrected for heart rate (QTc) \>= 470 ms calculated from 3 electrocardiograms (ECGs) using Bazett's correction * Current or prior use of immunosuppressive medication within 28 days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid * Any unresolved toxicity (\> CTCAE grade 2) from previous anti-cancer therapy; any prior grade \>= 3 immune-related adverse event (irAE) while receiving any previous immunotherapy agent, or any unresolved irAE \> grade 1 * Active or prior documented autoimmune disease within the past 2 years; NOTE: Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded * Active or prior documented inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis) * History of primary immunodeficiency * History of allogeneic organ transplant * History of hypersensitivity to durvalumab or any excipient * History of hypersensitivity to paclitaxel or carboplatin or their excipients * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diatheses including any subject known to have evidence of acute or chronic hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the subject to give written informed consent * Known history of previous clinical diagnosis of tuberculosis * History of leptomeningeal carcinomatosis * Receipt of live attenuated vaccination within 30 days prior to study entry or within 30 days of receiving durvalumab * Female subjects who are pregnant/breast-feeding or who are of reproductive potential and not employing acceptable methods of birth control; acceptable methods of contraception include true abstinence in line with the preferred and usual lifestyle choice of the patient, tubal ligation, vasectomized partner, barrier methods (e.g., cap plus spermicide, sponge plus spermicide, diaphragm plus spermicide, or male condom plus a spermicide), intrauterine device methods (e.g., Copper T or Levonorgestrel-releasing intrauterine system), or hormonal methods (e.g., any registered and marketed contraceptive agent that contains an estrogen and/or a progestational agent) and that is administered via the oral, subcutaneous, transdermal, intrauterine, or intramuscular route as an implant, hormone shot or injection, combined pill, minipill or patch; all methods of contraception should be used in combination with the use of a condom by their male sexual partner for intercourse * Any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results * Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive of but not limited to surgery, radiation and/or corticosteroids * Subjects with uncontrolled seizures