• Patients must have histologically or cytologically confirmed recurrent or metastatic HNSCC that is considered incurable.

• Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>=10 mm (\>= 1 cm) with CT scan, magnetic resonance imaging (MRI), or calipers by clinical exam.

• Primary tumor locations of oral cavity, oropharynx, hypopharynx, and larynx are allowed. Participants may not have a primary tumor site of nasopharynx.

• Patients with oropharyngeal cancer must have known human papillomavirus (HPV) status defined by human papillomavirus type 16 (p16) testing.

• Patients should not have had prior systemic therapy administered in the recurrent or metastatic setting. Systemic therapy which was given as part of multimodal treatment for locally advanced disease is allowed.

• Patients must be able to provide an archival tissue specimen.

• Patients must be willing to undergo a mandatory tumor biopsy on treatment

• Tumor tissue must have a documented combined positive score (CPS) of \>= 1 for PD-L1.

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of ipatasertib in combination with pembrolizumab in patients \< 18 years of age, children are excluded from this study.

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (Karnofsky \>= 60%).

• Absolute neutrophil count \>= 1,000/mcL.

• Platelets \>= 100,000/mcL.

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN).

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN.

• Creatinine =\< 1.5 x institutional ULN.

• Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 (using the Cockcroft-Gault formula).

• Human immunodeficiency virus (HIV) infected patients on effective antiretroviral therapy with undetectable viral load within 6 months are eligible for this trial.

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.

• Patients with a history of hepatitis C virus (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.

• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression.

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better.

• Patients must be able to swallow orally administered medication whole.

• For women of childbearing potential (WOCBP): agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \< 1% per year during the treatment period, for 5 months after the last dose of pembrolizumab and 28 days after the last dose of ipatasertib, and agreement to refrain from donating eggs during this same period.

• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, agreement to refrain from donating sperm during the treatment period, and for 5 months after the last dose of pembrolizumab and 28 days after the last dose of ipatasertib.

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible.