Targeting of histone methylation has therapeutic potential in oncology. Here, we provide proof-of-principle that pharmacological inhibition of KDM5 histone-demethylases is a new strategy for the personalized treatment of HER2+ breast cancer. The anti-proliferative effects of the prototype of a new class of selective KDM5-inhibitors (KDM5-inh1) are evaluated in 40 cell lines, recapitulating the heterogeneity of breast cancer. This analysis demonstrates that HER2+ cells are particularly sensitive to KDM5 inhibition. The results are confirmed in an appropriate in vivo model with a close structural analog (KDM5-inh1A). RNA-seq data obtained in HER2+ BT-474 cells exposed to KDM5-Inh1 indicate that the compound alters expression of numerous genes downstream of the ERBB2 gene-product, HER2. In selected HER2-positive breast-cancer cells, we demonstrate synergistic interactions between KDM5-inh1 and HER2-targeting agents (trastuzumab and lapatinib). In addition, HER2+ cell lines with innate and acquired resistance to trastuzumab show sensitivity to KDM5-inh1. The levels of KDM5A/B/C proteins, which are selectively targeted by the agent, have no significant association with KDM5-inh1 responsiveness across our panel of breast-cancer cell lines, suggesting the existence of other determinants of sensitivity. Using RNA-seq data of the breast-cancer cell lines we generate a gene-expression model that is a robust predictor of KDM5-inh1 sensitivity. In a test set of breast cancers, this model predicts sensitivity to the compound in a large fraction of HER2+ tumors. In conclusion, KDM5 inhibition has potential in the treatment of HER2+ breast cancer and our gene-expression model can be developed into a diagnostic tool for the selection of patients.