Zanubrutinib and Rituximab for the Treatment of Previously Untreated Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Patients must have a diagnosis chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) and be previously untreated * Patients must have an indication for treatment by 2018 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) Criteria * Patients must understand and voluntarily sign an informed consent, and be able to comply with study procedures and follow-up examinations * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Patients of childbearing potential must be willing to practice highly effective birth control (e.g., condoms, implants, injectables, combined oral contraceptives, intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) during the study and for 30 days after the last dose of study drug. Women of childbearing potential include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is not postmenopausal * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) except for patients with bilirubin elevation due to Gilbert's disease who will be allowed to participate * An alanine aminotransferase (ALT) =\< 2.5 x ULN * An estimated creatinine clearance (CrCl) of \> 30 mL/min, as calculated by the Cockcroft-Gault equation unless disease related * Free of prior malignancies for 3 years with exception of currently treated basal cell or squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast. If patients have another malignancy that was treated within the last 3 years, such patients can be enrolled, after consultation with the principal investigator, if the likelihood of requiring systemic therapy for this other malignancy within 2 years is less than 10%, as determined by an expert in that particular malignancy * A urine pregnancy test (within 7 days of day 1) is required for women with childbearing potential Exclusion Criteria: * Pregnant or breast-feeding females * Prior therapy with zanubrutinib or other kinase inhibitors that target BCR signaling (such as ibrutinib, idelalisib) * Prior CLL-directed treatment including chemotherapy, chemo-immunotherapy, monoclonal antibody therapy, radiotherapy, high-dose corticosteroid therapy (more than 60 mg prednisone daily or equivalent), or immunotherapy within 21 days prior to enrollment or concurrent with this trial. Patients that receive zanubrutinib salvage therapy cannot have received any other CLL-directed therapy besides frontline zanubrutinib plus rituximab * Investigational agent received within 30 days prior to the first dose of study drug. If received any investigational agent prior to this time point, drug-related toxicities must have recovered to grade 1 or less prior to first dose of study drug * Systemic fungal, bacterial, viral, or other infection not controlled by antimicrobial therapy, in the assessment of the treating physician(s) and/or the principal investigator * Patients with uncontrolled autoimmune hemolytic anemia (AIHA) or autoimmune thrombocytopenia (ITP), i.e. with laboratory signs of active hemolysis or thrombocytopenia, requiring support with blood products and/or with rapid decline in hemoglobin (\> 1 gram/dL per day) or platelet counts (\> 10,000/uL per day) * Patients with severe hematopoietic insufficiency, as defined by an absolute neutrophil count of less than 500/uL, unless disease-related, and/or a platelet count of less than 30,000/uL at time of screening for this protocol * Any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver or other organ system that may place the patient at undue risk to undergo therapy with zanubrutinib and rituximab * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification. Patients with a history of paroxysmal atrial fibrillation (PAF) or deep vein thrombosis or pulmonary embolism (DVT/PE) can be included if they had no signs of PAF or DVT/PE in the last 6 months before enrolment. Patients with ongoing atrial fibrillation (AFib) or ongoing PAF or DVT/PE should be excluded * History of stroke or cerebral hemorrhage within 6 months * Evidence of bleeding diathesis or coagulopathy within 3 months * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to day 1, anticipation of need for major surgical procedure during the course of the study * Minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to day 1. Bone marrow aspiration and/or biopsy are allowed * Serious, non-healing wound, ulcer, or bone fracture * Treatment with warfarin (Coumadin) or any other vitamin K antagonist. Patients who recently received warfarin must be off warfarin for at least 7 days prior to start of the study. Patients receiving novel oral anticoagulant (NOAC), also termed direct oral anticoagulant (DOAC) are permitted to enroll. Patients who are currently on a vitamin K antagonist must be switched to a non-vitamin K antagonist, such as a NOAC/DOAC * Patients with active hepatitis B (hepatitis B virus \[HBV\]) or hepatitis C * Patients with known human immunodeficiency virus (HIV) infection