Resistance to chemotherapy provides a major challenge in treatment of metastatic cancer. Prolonged exposure to almost any drug regimen leads to the formation of resistant subclones in almost all advanced solid tumors. Tumor heterogeneity because of intrinsic genetic instability is seen as one of the major contributing factors. In this work, we present evidence that genetic instability measured by mutation frequency is induced by treatment with the EGFR inhibitor afatinib or cisplatin in head and neck squamous cancer cells. We find that APOBEC3B and polymerase iota are upregulated, and inhibition of MEK1/2 by U0126 leads to downregulation on the protein level. Costimulation of afatnib and cisplatin with U0126 leads to a significantly lower mutation frequency. These findings may represent a molecular mechanism for dynamically controlling genetic instability during chemotherapy in head and neck squamous cell carcinoma (HNSCC) cancer cells.