Inclusion Criteria:

* Ability to understand and the willingness to sign a written informed consent document
* Age \>= 18 years at time of informed consent. Both men and women and members of all races and ethnic groups will be included
* Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
* Previously untreated therapy related myelodysplastic syndrome (t-MDS) with Revised International Prognostic Scoring System (IPSS-R) risk categories Intermediate, High or Very High (i.e., minimum IPSS-R score of 3.5) and presence of \< 20% bone marrow blasts per bone marrow biopsy/aspirate
* Patients with t-MDS which is defined as patients who have had prior anti-cancer therapy including chemotherapy and/or radiation therapy
* Aspartate aminotransferase (AST) \< 3.0 x upper limit of normal (ULN) x upper limit of normal (ULN; local laboratory)
* Alanine aminotransferase (ALT) \< 3.0 x ULN x ULN
* Total bilirubin =\< 2 x ULN (except for patients with known Gilbert's syndrome)
* Creatinine clearance \>= 30 mL/min OR serum creatinine \< 1.5 x the ULN
* White blood cell (WBC) count =\< 10,000/uL

* Note: Treatment with hydroxyurea is permitted to lower the WBC to reach this inclusion criterion. The WBC should be determined \>= 24 hours after the last dose of hydroxyurea. The last dose of hydroxyurea should not be administered =\< 3 days prior to the first dose of azacitidine
* Females of childbearing potential (FOCBP) must agree to adequate contraception (2 forms of contraception or abstinence) from the screening visit until 30 days following the last dose of venetoclax. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately

* FOCBP are those who have not been surgically sterilized or have not been free from menses for \> 1 year without an alternative medical cause
* Male patients of childbearing potential having intercourse with females of childbearing potential must agree to abstain from heterosexual intercourse or have their partner use 2 forms of contraception from the screening visit until 90 days after the last dose of study treatment. They must also refrain from sperm donation from the screening visit until 90 days following the last dose of study treatment

Exclusion Criteria:

* Participant has received prior therapy with a venetoclax or other BH3 mimetic. Note: Prior supportive care in form of transfusions or growth factors, etc., is not considered prior therapy. Supportive care should be discontinued \>= 14 days prior to the first dose of study drug. Subjects may continue oral corticosteroids for management of conditions other than MDS (e.g., asthma, rheumatoid arthritis) at a stable daily dose equivalent to =\< 10 mg prednisone during screening and study participation
* Subject has a diagnosis other than previously untreated de novo MDS with IPSS-R risk categories Intermediate, High or Very High, including:

* MDS with IPSS-R risk categories Very Low or Low (overall IPSS score \< 3)
* MDS evolving from a pre-existing myeloproliferative neoplasm (MPN)
* MDS/MPN including chronic myelomonocytic leukemia (CMML), atypical chronic myeloid leukemia (CML), juvenile myelomonocytic leukemia (JMML) and unclassifiable MDS/MPN
* Patients who are suitable for and willing to receive intensive chemotherapy or eligible to proceed to allogeneic stem cell transplantation without additional therapy
* Participant is seropositive with human immunodeficiency virus (HIV) or has active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV). HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. For patients with evidence of chronic HBV infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Individuals with a history of HCV infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Clinically significant ventricular arrhythmia (e.g., ventricular tachycardia, ventricular fibrillation, or Torsades de pointes)
* Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, myocardial infarction within 6 months prior to enrollment, New York Heart Association (NYHA) class III or IV heart failure
* Patients with uncontrolled infection will not be enrolled until infection is treated and under control
* Hypersensitivity to any study agent when administered alone. Any concurrent condition that, in the Investigator's opinion, would jeopardize the safety of the patient or compliance with the protocol
* Any psychiatric illness that prevents patient from informed consent process
* Pregnant of breastfeeding at the time of enrollment
* Subject has received allogeneic HSCT or solid organ transplantation
* Subject has a concurrent active malignancy requiring treatment or with an expected life expectancy less than 1 year with the exception of below. Any subject with a concurrent active malignancy will be reviewed by the PI for eligibility prior to enrollment

* Adequately treated in situ carcinoma of the cervix uteri
* Adequately treated basal cell carcinoma or localized squamous cell carcinoma of the skin
* Asymptomatic prostate cancer without known metastatic disease and with no requirement for therapy
* Subject exhibits evidence of other clinically significant uncontrolled condition(s) including, but not limited to:

* Ongoing systemic infection (viral, bacterial, or fungal)
* Acute pneumonia
* Febrile neutropenia
* Subject has received strong or moderate CYP3A inducers within 7 days prior to the first dose of study drug
* Subject has received strong or moderate CYP3A inhibitors within 7 days prior to the first dose of study drug
* Subject has consumed one or more of the following within 3 days prior to the first dose of study drug:

* Grapefruit or grapefruit products
* Seville oranges (including marmalade containing Seville oranges)
* Star fruit (carambola)
* Subject has a malabsorption syndrome or other condition that precludes an enteral route of administration
* Subject has history of a cardiovascular, endocrinologic, hepatic, immunologic metabolic, neurologic, psychiatric, pulmonary, renal disease, or any other condition that in the opinion of the investigator would adversely affect his/her participation in this study or interpretation of study results
* Subject has received a live attenuated vaccine within 4 weeks prior to the first dose of study drug