Paclitaxel and Ganetespib in Treating Patients With Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients with histologically or cytologically confirmed recurrent epithelial ovarian, fallopian tube or primary peritoneal cancers who have received up to two prior treatment regimens * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension in accordance with RECIST criteria version (v.) 1.1 * Patients must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound; this initial treatment may have included intraperitoneal therapy, high-dose therapy, consolidation, or extended therapy administered after completion of initial chemotherapy; patients must be considered platinum resistant or refractory according to standard Gynecologic Oncology Group (GOG) criteria, i.e., have had a treatment-free interval following platinum of less than 12 months, have persistent disease at the completion of primary platinum-based therapy or have progressed during platinum-based therapy * Eastern Cooperative Oncology Group (ECOG) performance status 0 -2 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< normal institutional limits * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) (serum glutamic oxaloacetic transaminase \[SGOT\]/serum glutamate pyruvate transaminase \[SGPT\]) =\< 2 times institutional normal limits * Creatinine =\< normal institutional limits OR * Creatinine clearance \>= 60 Ml/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Ability and willingness to comply with scheduled visits, treatment plan, laboratory assessments and other study procedures * Ability to understand and willingness to sign a written informed consent and Health Insurance Portability and Accountability Act (HIPAA) consent document Exclusion Criteria: * Patients who have had surgery, chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have toxicity that has not recovered to =\< grade 1 from adverse events due to agents administered more than 4 weeks earlier (with the exception of alopecia); patients may not be receiving any other investigational agents * Histologic diagnosis of a benign or borderline tumor ('tumor of low malignant potential') or of a malignant tumor of non-epithelial origin (such as a germ cell tumor, sex-cord stromal tumor) of the ovary, fallopian tube or peritoneum * Patients with known brain metastases * History of allergic reactions to Cremophor EL, paclitaxel or its components * Prior history of \>= grade 2 neurotoxicity or any other toxicity requiring discontinuation of taxane therapy that has not resolved to =\< grade 1, with the exception of alopecia * Diagnosis of another malignancy within two years before the first dose, or previously treated for another malignancy with evidence of residual disease, with the exception of a synchronous endometrial cancer; carcinoma in situ will not be considered as malignancy * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, known serious cardiac illness or psychiatric illness/social situations that would limit compliance with study requirements; known serious cardiac illness or medical conditions include, but are not limited to: * History of documented congestive heart failure (CHF), New York Heart Association (NYHA) class II/III/IV, with a history of dyspnea, orthopnea, or edema that requires current treatment with angiotensin-converting enzyme (ACE) inhibitors, angiotensin II receptor blockers, beta blockers, or diuretics * NOTE: use of these medications for the treatment of hypertension is allowed * Screening QTc (QT interval corrected for heart rate) \> 470 msec or history of QT (cardiac interval from start of Q wave to end of T wave) prolongation while taking other medications * High-risk uncontrolled arrhythmias (ventricular arrhythmias, high-grade atrioventricular \[AV\]-block, supra-ventricular arrhythmias that are not adequately rate-controlled) * Arrhythmias that require current treatment with the following anti-arrhythmic drugs: flecainide, moricizine, or propafenone * Current coronary artery disease with a history of myocardial infarction, angioplasty, or coronary bypass surgery within the preceding 6 months, or angina pectoris that has been symptomatic within the preceding 6 months * Known human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Pregnant or breast feeding