Pembrolizumab and Ibrutinib in Treating Patients With Stage III-IV Melanoma That Cannot Be Removed by Surgery

Inclusion Criteria: * PRE-REGISTRATION- INCLUSION CRITERIA * Diagnosis of unresectable stage III or metastatic melanoma (stage IV) not amenable to local therapy * At least one non-nodal lesion considered measurable by Response Evaluation Criteria in Solid Tumors (RECIST) criteria (that is, a lesion whose longest diameter can be accurately measured as \>= 1.0 cm with computed tomography \[CT\] scan, CT component of a positron emission tomography \[PET\]/CT, or magnetic resonance imaging \[MRI\]) or at least one malignant lymph node is considered measurable by RECIST criteria (that is, its short axis is \>= 1.5 cm when assessed by CT scan) * NOTE: tumor lesions in a previously irradiated area are not considered measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Provide informed written consent * Patient is willing to undergo treatment and monitoring at the enrolling institution * Willing to provide tissue and blood samples for correlative research purposes * REGISTRATION- INCLUSION CRITERIA * Histologic or cytologic confirmation of unresectable stage III or metastatic melanoma (stage IV) not amenable to local therapy * Only if patient has had previous exposure to anti-PD-1 or anti-PD-L1 therapy: * Patient had disease progression on or within 6 months after anti-PD-1/anti-PD-L1 therapy in the metastatic setting OR * Patient had disease progression within 6 months after the last dose of adjuvant/neoadjuvant anti-PD-1/anti-PD-L1 treatment * Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 75,000/mm\^3 (obtained =\< 14 days prior to registration) * Criteria must be met without a transfusion =\< four weeks prior to registration * Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 X upper limit of normal (ULN); if total bilirubin \> 1.5 X ULN then direct bilirubin =\< ULN (obtained =\< 14 days prior to registration) * Aspartate aminotransferase (aspartate transaminase \[AST\]) and alanine aminotransferase (alanine transaminase \[ALT\]) =\< 2.5 x ULN OR =\< 5 X ULN for patients with liver metastases (obtained =\< 14 days prior to registration) * Creatinine =\< 1.5 X ULN and creatinine clearance (CrCL) \>= 30 ml/min per Cockcroft Gault formula (obtained =\< 14 days prior to registration) * Patients of childbearing potential only, negative urine pregnancy test done =\< 7 days prior to study registration Exclusion Criteria: * PRE-REGISTRATION EXCLUSION CRITERIA * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study medication; adequate contraception is defined as 2 methods of birth control (e.g., hormonal contraceptives, intrauterine device, diaphragm with spermicide, cervical cap with spermicide, male condoms, or female condom with spermicide) or prior surgical sterilization, or abstinence from heterosexual activity * Prior treatment with ibrutinib or prior exposure to BTK inhibitors * Uveal melanoma * Current use of warfarin or other vitamin K antagonists * Require continuous treatment with a strong CYP3A inhibitor * Currently participating or has participated in a study of an investigational cancer therapy agent or using an investigational device within 28 days prior to study registration * Live vaccines within 28 days prior to study pre-registration * Invasive surgical procedure within 28 days prior to study pre-registration * History of clinically severe (e.g., requires chronic immunosuppressive therapy, \[e.g., cyclosporine A, tacrolimus\]) autoimmune disease (e.g., ulcerative colitis, lupus), or history of organ transplant * Known history of human immunodeficiency virus (HIV) infection, active infection with hepatitis B virus or hepatitis C virus, or any uncontrolled active systemic infection * Gastrointestinal disease that might inhibit ibrutinib absorption (e.g., malabsorption syndrome, resection of the stomach or a large portion of small bowel, or partial/complete bowel obstruction), or unable to swallow capsules * Active central nervous system metastases and/or carcinomatous meningitis * Note: Patients with untreated brain metastasis will be excluded; patients with previously treated brain metastases may participate provided they meet the following criteria: * Inactive (without evidence of progression which is documented by CT or MRI within 90 days prior to registration), AND * On =\< 10 mg/day prednisone or equivalent for at least 28 days prior pre-registration * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Clinically significant cardiovascular disease such as unstable angina, myocardial infarction, or acute coronary syndrome within =\< 180 days prior to registration, symptomatic or uncontrolled arrhythmia, congestive heart failure, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification * Other active malignancy =\< 3 years prior to pre-registration; note: if there is a history of prior malignancy, the patient must not be receiving other specific treatment for cancer * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome =\< 6 months prior to pre-randomization * Known bleeding disorders (von Willebrand's disease or hemophilia) * History of ischemic stroke or intracranial hemorrhage =\< 180 days prior to pre-registration * Currently active, clinically significant hepatic impairment Child-Pugh class A, B or C according to the Child Pugh classification * Unresolved toxicities from prior anti-cancer therapy, defined as not resolved to Common Terminology Criteria for Adverse Events (CTCAE, version \[v\]4.0) grade 0 or 1, or to the levels dictated in the inclusion/exclusion criteria with the exceptions of alopecia and peripheral neuropathy * REGISTRATION- EXCLUSION * Failure to confirm histologically or cytologically unresectable stage III or metastatic melanoma (stage IV) not amenable to local therapy * Prior chemotherapy, immunotherapy, radioactive, or biological cancer therapy (including monoclonal antibody \[mAb\]) =\< 28 days prior to registration * Received a strong cytochrome P450 (CYP) 3A inhibitor =\< 7 days prior to registration * Concurrent systemic immunosuppressant therapy =\< 21 days prior to registration * Recent infection requiring systemic antibiotic treatment that was completed =\< 14 prior to registration