Pevonedistat With Azacitidine Versus Azacitidine Alone in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients must have an established and confirmed diagnosis of AML by World Health Organization (WHO) criteria, excluding acute promyelocytic leukemia (APL). * Patients must have relapsed or refractory AML, defined as: * Relapsed: \>= 5% bone marrow blasts by morphology, reappearance of minimal residual disease (MRD) (\> 0.1%) by flow cytometry, reappearance of peripheral blood blasts, or development of extramedullary leukemia after one or more prior lines of therapy. Consolidation regimens, including autologous and allogeneic HCT, do not count as a separate prior line of therapy, (e.g., 7+3 followed by cytarabine consolidation followed by allogeneic hematopoietic cell transplantation (HCT) would be considered one prior line of therapy). Note, there is no restriction on the prior number of relapses and prior treatment of relapsed disease is allowed. * Refractory: no complete response (CR) or complete response with incomplete bone marrow recovery (CRi) after two courses of induction therapy (e.g. therapy with the intent to induce remission). Patients 75 years or older, or patients of any age with comorbidities that prevent the use of further intensive chemotherapy, will be eligible if they did not experience CR or CRi after one course of induction therapy. * Patients must have Karnofsky \>= 60%. * Patients must have a white blood cell count (WBC) =\< 25 x 10\^9 cells/L. Hydroxyurea and leukapheresis are permitted to satisfy this criterion. * Total bilirubin =\< institutional upper limit of normal (ULN) except in patients with Gilbert's syndrome or post-transfusion hemolysis. Patients with Gilbert's syndrome or post-transfusion hemolysis may enroll if direct bilirubin =\< 1.5 x ULN of the direct bilirubin. * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN (unless resulting from liver infiltration with leukemia). * Creatinine clearance \>= 30 mL/min (If serum creatinine not =\< institutional ULN). * Hemoglobin \> 8 g/dL. Patients may be transfused to achieve this value. * Human immunodeficiency virus (HIV)-infected patients will be eligible for this trial if they are on effective antiretroviral regimens utilizing non-CYP-interacting agents, they have an undetectable viral load, they have a CD4 count \> 350 cells/mm\^3, and they have no history of acquired immune deficiency syndrome (AIDS)-defining opportunistic infections. If there is evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable on suppressive therapy, if indicated. If there is history of hepatitis C virus (HCV) infection, the patient must have been treated and have undetectable HCV viral load. * Patients must be willing to submit blood samples for the integrated biomarker. * Female patients of childbearing potential (i.e. who are not postmenopausal for at least 1 year before screening or are not surgically sterile) must have a negative serum pregnancy test within 72 hours prior to the first study drug administration and must agree to practice one highly effective method and one additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug, or agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient. Male patients, even if surgically sterilized, must agree to practice effective barrier contraception during the entire study treatment period through 4 months after the last dose of study drug, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, postovulation methods), withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. * Patients may have had prior allogeneic HCT at least 3 months prior to randomization but should not have evidence of active graft versus host disease or require systemic immune suppression. * Patients must be able to understand and be willing to sign a written informed consent document. * Patients with impaired decision-making capacity (IDMC) will be eligible if they have a legal guardian or a close family member available to assist them. Exclusion Criteria: * Patients must not have had prior treatment with MLN4924 (pevonedistat), azacitidine, or decitabine. * Patients for whom, in the opinion of the treating physician, azacitidine alone is not an appropriate treatment will be excluded. * Patients must not have documented active central nervous system (CNS) involvement by leukemia. Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Patients must not have received any other investigational or commercial agents or therapies administered with the intention to treat their leukemia within 14 days or five half-lives (whichever is shorter) of first receipt of study drug, with the exception of hydroxyurea used to control WBCs. * All non-hematologic adverse events (AEs) of prior chemotherapy, surgery, or radiotherapy, except alopecia, must have resolved to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade =\< 2 prior to starting therapy. * Patients must not have a history of other malignancies, except: * Any malignancy that was treated with curative intent, has no known active disease present for \>= 1 year before the first dose of study drug, and is felt to be at low risk of recurrence by the treating physician; * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease; * Adequately treated carcinoma in situ without evidence of disease; * Low-risk prostate cancer after curative surgery. * Patients must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to MLN4924 (pevonedistat), azacitidine, or mannitol. * Clinically significant metabolic enzyme inducers are not permitted during this study, or within 14 days before the first dose of study drugs. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Patients must not have severe and/or uncontrolled medical conditions or other conditions that, in the opinion of the investigator, could affect their participation in the study. * Pregnant women are ineligible because, as an Nedd8 activating enzyme (NAE) inhibitor, MLN4924 (pevonedistat) has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with MLN4924 (pevonedistat), breastfeeding must be discontinued if the mother is treated with MLN4924 (pevonedistat). These potential risks may also apply to azacitidine. * Patients must not have had major surgery within 14 days before the first dose of any study drug or be scheduled for surgery during the study period. * Patients must not have uncontrolled coagulopathy or a bleeding disorder unless directly attributable to their AML (e.g., disseminated intravascular coagulation). * Patients must not have known hepatic cirrhosis or severe pre-existing hepatic impairment. * Patients must not have known cardiopulmonary disease defined as: * Unstable angina; * Congestive heart failure (New York Heart Association \[NYHA\] class III or IV; * Myocardial infarction (MI) within 6 months prior to first dose. Patients who had ischemic heart disease such as acute coronary syndrome (ACS), MI, and/or revascularization more than 6 months before screening and who are without cardiac symptoms or those with a prior non-ST elevation MI due to demand-supply mismatch (NSTEM type II) may enroll; * Symptomatic cardiomyopathy; * Clinically significant arrhythmia: * History of polymorphic ventricular fibrillation or torsade de pointes, * Permanent atrial fibrillation, defined as continuous atrial fibrillation lasting for \>= 6 months; * Persistent atrial fibrillation, defined as sustained atrial fibrillation lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening; * Grade 3 atrial fibrillation, defined as symptomatic and incompletely controlled medically, or controlled with a device (e.g., pacemaker) or by ablation; * Patients with paroxysmal atrial fibrillation or \< grade 3 atrial fibrillation for period of at least 6 months are permitted to enroll provided that their heart rate is controlled on a stable regimen; * Moderate or severe pulmonary hypertension. * Patients must not have uncontrolled high blood pressure that cannot be controlled by standard therapies. * Patients must not have any life-threatening illness unrelated to cancer. * Patients must not have an active, uncontrolled infection or severe infectious disease, (e.g. severe pneumonia, meningitis, or septicemia). Patients with an uncontrolled infection must not be enrolled until they have received treatment and the infection is under control. * Patients must not have prolonged rate-corrected QT (QTc) interval \>= 480 msec, calculated according to institutional guidelines. * Patients must not have left ventricular ejection fraction \< 40% as assessed by a transthoracic echocardiogram or radionuclide angiography within one month prior to study entry. * Patients must not have known moderate to severe chronic obstructive pulmonary disease, interstitial lung disease, or pulmonary fibrosis. * Female patients who intend to donate eggs (ova) during the course of this study or within 4 months of receiving their last dose of study drugs are ineligible. * Male patients who intend to donate sperm during the course of this study or within 4 months of receiving their last dose of study drugs are ineligible.