Therapeutics such as lapatinib that target ERBB2 often provide initial clinical benefit but resistance frequently develops. Adaptive responses leading to lapatinib resistance involve reprogramming of the kinome through reactivation of ERBB2/ERBB3 signaling and transcriptional upregulation and activation of multiple tyrosine kinases. The heterogeneity of induced kinases prevents their targeting by a single kinase inhibitor, underscoring the challenge of predicting effective kinase inhibitor combination therapies. We hypothesized that to make the tumor response to single kinase inhibitors durable, the adaptive kinome response itself must be inhibited. Genetic and chemical inhibition of BET bromodomain chromatin readers suppresses transcription of many lapatinib-induced kinases involved in resistance including ERBB3, IGF1R, DDR1, MET, and FGFRs, preventing downstream SRC/FAK signaling and AKT reactivation. Combining inhibitors of kinases and chromatin readers prevents kinome adaptation by blocking transcription, generating a durable response to lapatinib and overcoming the dilemma of heterogeneity in the adaptive response. Display omitted Lapatinib induces heterogeneous RTK-based kinome adaptation in ERBB2+ cellsMultiple unrelated kinases contribute to cell growth in the presence of lapatinibBET bromodomain inhibition suppresses expression of lapatinib-induced kinasesTargeting kinome adaptation makes kinase inhibition durable