Most tumor types either fail to respond or become resistant to kinase inhibitors, often because of compensatory prosurvival pathways in the cancer cell's broader signaling circuitry. Here, we found that intrinsic resistance to kinase inhibitors in cultured primary acute myeloid leukemia (AML) cells may be overcome by reshaping kinase networks into topologies that confer drug sensitivity. We identified several antagonists of chromatin-modifying enzymes that sensitized AML cell lines to kinase inhibitors. Of these, we confirmed that inhibitors of the lysine-specific demethylase (LSD1; also known as KDM1A) rewired kinase signaling in AML cells in a way that increased the activity of the kinase MEK and that broadly suppressed the activity of other kinases and feedback loops. As a result, AML cell lines and about half of primary human AML samples were primed for sensitivity to the MEK inhibitor trametinib. Primary human cells with KRAS mutations and those with high MEK pathway activity were the best responders to sequential treatment with LSD1 inhibitors then trametinib, whereas those with NRAS mutations and high mTOR activity were poor responders. Overall, our study reveals the MEK pathway as a mechanism of resistance to LSD1 inhibitors in AML and shows a way to modulate kinase network circuitry to potentially overcome therapeutic resistance to kinase inhibitors.