The worldwide frequency of head and neck squamous cell carcinoma (HNSCC) is approximately 800,000 new cases, with 430,000 deaths annually. We determined that LZK (encoded by MAP3K13) is a therapeutic target in HNSCC and showed that inhibition with small molecule inhibitors decreases the viability of HNSCC cells with amplified MAP3K13. A drug-resistant mutant of LZK blocks decreases in cell viability due to LZK inhibition, indicating on-target activity by two separate small molecules. Inhibition of LZK catalytic activity suppressed tumor growth in HNSCC PDX models with amplified MAP3K13. We found that the kinase activity of LZK stabilized c-MYC and that LZK stabilized gain-of-function (GOF) p53 through a kinase-independent mechanism. Therefore, we designed proteolysis-targeting chimeras (PROTACs) and demonstrate that our lead PROTAC promotes LZK degradation and suppresses expression of GOF p53 and c-MYC leading to impaired viability of HNSCC cell lines. This research provides a strong basis for development of therapeutics targeting LZK in HNSCCs with amplification of the gene.