The loss of p16 is a signature event in Human Papilloma Virus (HPV)-negative head and neck squamous cell carcinoma (HNSCC) that leads to increased Cyclin Dependent Kinase 4/6 (CDK) signaling. Palbociclib, a CDK4/6 inhibitor, is active for the treatment of a subset of HNSCC. In this study, we analyzed patient response data from a phase I clinical trial of palbociclib in HNSCC and observed an association between prior cisplatin exposure and CDK inhibitor resistance. We studied the effects of palbociclib on cisplatin-sensitive and -resistant HNSCC cell lines. We found that while palbociclib is highly effective against chemo-naive HNSCC cell lines and tumor xenografts, prior cisplatin exposure induces intrinsic resistance to palbociclib in vivo, a relationship that was not observed in vitro. Mechanistically, in the course of provoking a DNA damage-resistance phenotype, cisplatin exposure upregulates both c-Myc and cyclin E, and combination treatment with palbociclib and the c-Myc bromodomain inhibitor JQ1 exerts a synergistic anti-growth effect in cisplatin-resistant cells. These data show the benefit of exploiting the inherent resistance mechanisms of HNSCC to overcome cisplatin- and palbociclib resistance through the use of c-Myc inhibition.