Therapeutic resistance in cancer is often assumed to involve acquired genetic mutations. There is, however, increasing evidence that epigenetic mechanisms also contribute to therapeutic escape and is a major mechanism of resistance in over 30% of patients with cancers such as AML. Molecular insights into the transcriptional adaptation that underpins non-genomic resistance are unclear. It is also unknown whether this adaptive response is stable and can be overcome. Using single cell RNA-sequencing of paired drug naïve and drug resistant AML patient samples and cellular barcoding in a unique mouse model of non-genetic resistance, we demonstrate that a form of Lamarckian evolution, namely transcriptional plasticity, drives stable epigenetic resistance. With a CRISPR- Cas9 screen, we identify regulators of enhancer function, as important modulators of the resistant cell state. This enhancer remodelling does not result in a simple linear reversion to the original transcription state of drug naïve cells. Instead, the newly formed enhancers become essential in sustaining the expression of a key subset of genes required for cell survival. Together these findings highlight the underappreciated role of transcriptional adaptation in mediating resistance to cancer therapies at the time of clinical remission. They also provide new molecular insights and therapeutic opportunities to counteract this process.