Head and neck squamous cell carcinomas (HNSCC) affect more than 800,000 people annually worldwide, causing over 15,000 deaths in the US. Among HNSCC cancers, human papillomavirus (HPV)-negative HNSCC has the worst outcome, motivating efforts to improve therapy for this disease. The most common mutational events in HPV-negative HNSCC are inactivation of the tumor suppressors TP53 (>85%) and CDKN2A (>57%), which significantly impairs G1/S checkpoints, causing reliance on other cell cycle checkpoints to repair ongoing replication damage. We evaluated a panel of cell cycle-targeting clinical agents in a group of HNSCC cell lines to identify a subset of drugs with single-agent activity in reducing cell viability. Subsequent analyses demonstrated potent combination activity between the CHK1/2 inhibitor LY2606268 (prexasertib), which eliminates a G2 checkpoint, and the WEE1 inhibitor AZD1775 (adavosertib), which promotes M-phase entry, in induction of DNA damage, mitotic catastrophe, and apoptosis, and reduction of anchorage independent growth and clonogenic capacity. These phenotypes were accompanied by more significantly reduced activation of CHK1 and its paralog CHK2, and enhanced CDK1 activation, eliminating breaks on the mitotic entry of cells with DNA damage. These data suggest the potential value of dual inhibition of CHK1 and WEE1 in tumors with compromised G1/S checkpoints.