Non-small-cell lung cancer is the leading cause of cancer-related death worldwide. Chemotherapies such as the topoisomerase II (TopoII) inhibitor etoposide effectively reduce disease in a minority of patients with this cancer; therefore, alternative drug targets, including epigenetic enzymes, are under consideration for therapeutic intervention. A promising potential epigenetic target is the methyltransferase EZH2, which in the context of the polycomb repressive complex 2 (PRC2) is well known to tri-methylate histone H3 at lysine 27 (H3K27me3) and elicit gene silencing. Here we demonstrate that EZH2 inhibition has differential effects on the TopoII inhibitor response of non-small-cell lung cancers in vitro and in vivo. EGFR and BRG1 mutations are genetic biomarkers that predict enhanced sensitivity to TopoII inhibitor in response to EZH2 inhibition. BRG1 loss-of-function mutant tumours respond to EZH2 inhibition with increased S phase, anaphase bridging, apoptosis and TopoII inhibitor sensitivity. Conversely, EGFR and BRG1 wild-type tumours upregulate BRG1 in response to EZH2 inhibition and ultimately become more resistant to TopoII inhibitor. EGFR gain-of-function mutant tumours are also sensitive to dual EZH2 inhibition and TopoII inhibitor, because of genetic antagonism between EGFR and BRG1. These findings suggest an opportunity for precision medicine in the genetically complex disease of non-small-cell lung cancer.