Bromodomain and extra-terminal domain (BET) family inhibitors offer an approach to treating hematological malignancies. We used precision nuclear run-on transcription sequencing (PRO-seq) to create high-resolution maps of active RNA polymerases across the genome in t(8;21) acute myeloid leukemia (AML), as these polymerases are exceptionally sensitive to BET inhibitors. PRO-seq identified over 1,400 genes showing impaired release of promoter-proximal paused RNA polymerases, including the stem cell factor receptor tyrosine kinase KIT that is mutated in t(8;21) AML. PRO-seq also identified an enhancer 3′ to KIT. Chromosome conformation capture confirmed contacts between this enhancer and the KIT promoter, while CRISPRi-mediated repression of this enhancer impaired cell growth. PRO-seq also identified microRNAs, including MIR29C and MIR29B2, that target the anti-apoptotic factor MCL1 and were repressed by BET inhibitors. MCL1 protein was upregulated, and inhibition of BET proteins sensitized t(8:21)-containing cells to MCL1 inhibition, suggesting a potential mechanism of resistance to BET-inhibitor-induced cell death.