Non-genetic drug resistance is increasingly recognised in various cancers. Molecular insights into this process are lacking and it is unknown whether stable non-genetic resistance can be overcome. Using single cell RNA-sequencing of paired drug naïve and resistant AML patient samples and cellular barcoding in a unique mouse model of non-genetic resistance, here we demonstrate that 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. We show that inhibition of Lsd1 (Kdm1a) is able to overcome stable epigenetic resistance by facilitating the binding of the pioneer factor, Pu.1 and cofactor, Irf8, to nucleate new enhancers that regulate the expression of key survival genes. This enhancer switching results in the re-distribution of transcriptional co-activators, including Brd4, and provides the opportunity to disable their activity and overcome epigenetic resistance. Together these findings highlight key principles to help counteract non-genetic drug resistance.