Pembrolizumab and Carboplatin for the Treatment of Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Have a diagnosis of ovarian, fallopian tube, or primary peritoneal cancer who have received systemic chemotherapy including platinum-based chemotherapy * Have a cancer antigen (CA)-125 that normalized after first-line therapy * CA-125 increased to more than twice the upper limit of normal or two times the nadir value after most recent second or later line of treatment * Have no measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Ascites and pleural effusions are not measurable disease, if asymptomatic * All patients who are having sex that can lead to pregnancy must agree to contraception for the duration of the study * Have estimated life expectancy of at least 3 months * Be willing and able to provide written informed consent/assent for the trial * Be \>= 18 years of age on day of signing informed consent * Have a performance status of 0 or 1 on the on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL (performed within 14 days of treatment initiation) * Platelets \>= 100,000/mcL (performed within 14 days of treatment initiation) * Hemoglobin (Hgb) \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) (performed within 14 days of treatment initiation) * Creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 30 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (performed within 14 days of treatment initiation) * Total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 X ULN (performed within 14 days of treatment initiation) * Aspartate transaminase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine transferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases (performed within 14 days of treatment initiation) * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless patient is receiving anticoagulant therapy (as long as PT or partial thromboplastin time \[PTT\] is within therapeutic range of intended use of anticoagulants) (performed within 14 days of treatment initiation) * Activated partial thromboplastin time (aPTT) or PTT =\< 1.5 X ULN unless patient is receiving anticoagulant therapy (as long as PT or PTT is within therapeutic range of intended use of anticoagulants) (performed within 14 days of treatment initiation) Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (if dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Short-term administration of systemic steroids (i.e., for allergic reactions or the management of immune-related adverse events \[irAEs\]) is allowed * Has symptomatic ascites or pleural effusions * History of borderline or low malignant potential ovarian cancer * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) 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, biologic therapy, targeted small molecule therapy, hormonal 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: Patients with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: If a patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least 4 weeks prior to the first dose of trial 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 14 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 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 a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or current pneumonitis/interstitial lung disease * 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 trial, interfere with the patient's participation for the full duration of the trial, or is not in the best interest of the patient 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 trial * Is pregnant or breastfeeding, or expecting to conceive children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Clinically significant cardiovascular disease * Known severe hypersensitivity reactions to monoclonal antibodies or carboplatin \>= grade 3, any history of anaphylaxis, or uncontrolled asthma * Has received prior therapy with pembrolizumab * 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 or live-attenuated vaccine within 30 days of planned start of study therapy. Administration of killed vaccines is allowed * Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines and are not allowed