Pembrolizumab, Carboplatin, and Paclitaxel in Treating Patients With Stage III-IV Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Signed, written informed consent * Histology showing high-grade epithelial non-mucinous ovarian, primary peritoneal, or fallopian tube cancer * No more than 4 prior cycles of chemotherapy for primary advanced (stage III or IV) epithelial ovarian, primary peritoneal, or fallopian tube cancer * No prior treatment involving irradiation, hormonal therapy, immunotherapy, investigational therapy, and/or other concurrent agents or therapies for ovarian cancer * A disposition to neoadjuvant chemotherapy with planned interval tumor reductive surgery after 4 complete cycles of treatment * Planned dose-dense chemotherapy with combination carboplatin and paclitaxel given intravenously * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 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 * Peripheral neuropathy grade 0 or 1 by National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 * Tissue from an archival tissue sample or fresh tissue obtained from a core or excisional biopsy of a tumor lesion * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500 /mcL * Platelets \>= 100,000/mcL * Hemoglobin (Hgb) \>= 9 g/dL or \>= 5.6 mmol/L * Creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with liver metastases * International normalized ratio (INR)/prothrombin time (PT) =\< 1.5 x ULN (unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time \[PTT\] is within therapeutic range of intended use of anticoagulants) * PTT =\< 1.5 x ULN (unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants) * Women of child-bearing potential (intact uterus) should have a negative urine or serum pregnancy within 72 hours prior to receiving the first 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; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * 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; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Pre-treatment fresh frozen tissue available for research purposes; this tissue can be collected from preoperative laparoscopy, other diagnostic biopsy, or a research-specific biopsy * Signed informed consent on protocol LAB02-188 Exclusion Criteria: * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment * Histology showing mucinous or low grade epithelial ovarian carcinoma * 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 or low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease e.g., cervical cancer in situ * Concomitant stage 1A/B, grade 1-2 endometrioid endometrial cancer as allowable contemporary tumor * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of study treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to study treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) * Patients with ovarian cancer not medically fit for diagnostic laparoscopy prior to initiation of therapy * Patients with any evidence of severe or uncontrolled systemic disease (e.g. severe hepatic impairment, interstitial lung disease \[bilateral, diffuse, parenchymal lung disease\], uncontrolled chronic renal disease \[glomerulonephritis, nephritic syndrome, Fanconi syndrome or renal tubular acidosis\]), or current unstable or uncompensated respiratory or cardiac conditions, or uncontrolled hypertension blood pressure \>= 140/90, active bleeding diatheses or active infection * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study; Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * No active autoimmune disease that has required systemic treatment in past two years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc) is not considered a form of systemic treatment * Has evidence of interstitial lung disease or active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the pre-screening or screening visit through 120 days after the last dose of study treatment * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of study treatment * Patients with tuberculosis * Patients with known hypersensitivity to pembrolizumab or any of its excipients * Patients receiving concurrent additional biologic therapy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to carboplatin, paclitaxel not responsive to traditional desensitization procedures * 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