Histone lysine methyltransferase 2D (KMT2D) is the most frequently mutated epigenetic modifier in head and neck squamous cell carcinoma (HNSCC). However, the role of KMT2D in HNSCC tumorigenesis and whether its mutations confer any therapeutic vulnerabilities remain unknown. Here we show that KMT2D deficiency promotes HNSCC growth through increasing glycolysis. Additionally, KMT2D loss decreases the expression of Fanconi Anemia (FA)/BRCA pathway genes under glycolytic inhibition. Mechanistically, glycolytic inhibition facilitates the occupancy of KMT2D to the promoter/enhancer regions of FA genes. KMT2D loss reprograms the epigenomic landscapes of FA genes by transiting their promoter/enhancer states from active to inactive under glycolytic inhibition. Therefore, combining the glycolysis inhibitor 2-DG with DNA crosslinking agents or poly (ADP-ribose) polymerase (PARP) inhibitors preferentially inhibits tumor growth of KMT2D-deficient mouse HNSCC and patient-derived xenografts (PDXs) harboring KMT2D-inactivating mutations. These findings provide an epigenomic basis for developing targeted therapies for HNSCC patients with KMT2D-inactivating mutations.