Therapeutic resistance in cancer has long been assumed to involve genetic mutations. However, epigenetic mechanisms are emerging as an important component of cancer resistance. Insights into the cellular and molecular mechanisms that mediate non-genomic resistance are lacking, specifically, it is unclear whether epigenetic resistance occurs through selection for pre-existing subpopulations or through drug-induced transcriptional adaptation. It is also largely unknown whether this adaptive response is stable and can be overcome. To explore the potential role of non-genomic resistance in AML, we interrogated published genomic datasets and performed single cell RNA-sequencing of paired drug naïve and drug resistant patient samples. These data suggest that non-genomic resistance is a pervasive clinical feature in AML and can arise through either selection for pre-existing epigenetic heterogeneity or via transcriptional plasticity. Through in vitro cellular barcoding and scRNA-seq, we provide conclusive evidence that gradual Lamarckian transcriptional adaptation can drive stable epigenetic resistance to BET bromodomain inhibitors. Using this unique model, we subsequently demonstrate that non-genomic resistance can be overcome through inhibition of the histone demethylase, LSD1, which triggers new enhancer activation. Mechanistically, we find that LSD1 inhibition causes new enhancer formation by de-repressing Irf8, which acts to stabilize the pioneer factor, Pu.1, at chromatin. This enhancer remodeling redistributes the co-activators, Brd4 and Med1, to new enhancers located around key genes required for AML survival, reinstating the resistant cells sensitivity to BET inhibitors. Together these findings highlight the underappreciated role of transcriptional adaptation in mediating resistance to cancer therapies and suggest a role for epigenetic therapies in reprogramming cancer cells to avoid or overcome non-genomic resistance.