Inclusion Criteria:

* Morphologically confirmed diagnosis of acute myeloid leukemia (AML) with classification other than WHO acute promyelocytic leukemia (FAB M3), based on bone marrow examination performed within 14 days prior to registration; patients with World Health Organization (WHO) acute promyelocytic leukemia (FAB M3) or blastic transformation of chronic myelogenous leukemia are not eligible
* Zubrod performance status 0-3
* No known hypersensitivity to azacitidine, mannitol, hydroxyurea, orgemtuzumab ozogamicin
* No prior systemic chemotherapy for acute leukemia with the exception of hydroxyurea; administration of hydroxyurea to control high white blood cell (WBC) count prior to registration is permitted
* Patients with a history of prior myelodysplastic syndrome (MDS) are eligible according to the following criteria:

* No prior treatment of MDS with AML induction-type chemotherapy or high-dose chemotherapy with hematopoietic stem cell support
* Prior cytarabine allowed if dose \< 100 mg/m\^2/day
* Prior hematopoietic growth factors, thalidomide, lenalidomide, arsenic trioxide, and signal transduction inhibitors for treatment of MDS allowed
* No prior treatment with azacitidine, decitabine, or gemtuzumab ozogamicin
* At least 30 days since prior therapy for MDS and recovered
* Bilirubin =\< 2.0 x institutional upper limit of normal (IULN) within 14 days to registration, unless the elevation is believed to be due to hepatic infiltration by AML

* Hyperbilirubinemia due primarily to elevated unconjugated hyperbilirubinemia secondary to Gilbert syndrome or hemolysis is allowed
* Serum glutamic oxaloacetic transaminase (SGOT) aspartate aminotransferase (AST) =\< 2 x IULN, or serum glutamic pyruvate transaminase (SGPT) alanine aminotransferase (ALT) =\< 2.0 x IULN , unless the elevation is believed to be due to hepatic infiltration by AML
* Serum creatinine =\< 1.5 x IULN
* Left ventricle ejection fraction (LVEF) \>= 40% by multi-gated acquisition scan (MUGA) or echocardiogram (ECHO) AND no clinical evidence of congestive heart failure within the past 56 days
* Pretreatment cytogenetics must be performed on all patients; collection of pretreatment specimens must be completed within 14 days prior to registration to S0703; specimens must be submitted to the site's preferred cytogenetics laboratory
* Patients must consent to submit specimens to the Southwest Oncology Group (SWOG) acute lymphoblastic leukemia (ALL)/chronic lymphocytic leukemia (CLL)/chronic myelogenous leukemia (CML) repository for cellular and molecular studies; collection of pretreatment blood and/or marrow specimens must be completed within 14 days prior to registration; if a marrow specimen is available, either from the diagnostic marrow or a repeat pre-registration marrow, then it must be submitted along with a peripheral blood specimen; otherwise peripheral blood alone must be submitted; residual specimens will only be banked if the patient provides separate consent; sites are required to offer patients the opportunity to participate in banking
* No central nervous system (CNS) involvement; if central nervous involvement is clinically suspected, it must be ruled out by a lumbar puncture
* Women of reproductive potential must have a pregnancy test within 28 days prior to registration; patients must not be pregnant or nursing because of the teratogenic potential of the drugs used in this study; women/men of reproductive potential must have agreed to use an effective contraceptive method
* Patients not known to be human immunodeficiency virus positive (HIV+) must be tested for HIV infection within 14 days prior to registration
* HIV-positive patients must meet the following criteria:

* No history of acquired immunodeficiency syndrome (AIDS)-defining events
* CD4 cells \>= 500/mm\^3
* Viral load of \< 50 copies HIV messenger ribonucleic acid (mRNA)/mm\^3 if on cART or \< 25,000 copies HIV mRNA if not on cART
* No zidovudine or stavudine as part of cART Patients who are HIV+ and do not meet all of these criteria will not be eligible for this study
* No other prior malignancy except for a) adequately treated basal cell or squamous cell skin cancer or b) any diagnosis of malignancy made within the past 2 years earlier, of which there is no clinically evident cancer, and for which the patient has completed all chemotherapy and radiotherapy at least 6 months prior to study registration; prior treatment with AML induction-type chemotherapy is not allowed; concurrent hormonal therapy is allowed
* All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* At the time of patient registration, the treating institution's name and identification (ID) number must be provided to the Data Operations Center in Seattle in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the data base
* Patients must have complete remission (CR) or CRi, documented by blood and marrow examinations performed within 42 days before this registration
* Following completion of induction therapy, the blood counts must recover to absolute neutrophil count (ANC) \>= 1,000/mcL and platelets \>= 90,000/mcL (without transfusion), and must be maintained at these levels during the 7 days prior to registration
* Patients must have serum creatinine =\< 1.5 x IULN and SGOT or SGPT =\< 1.5 x IULN within 28 days before registration
* Patients must have recovered to =\< Grade 2 from any induction cycle non-hematologic toxicities