Acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL) are life‐threatening hematopoietic malignancies characterized by clonal expansion of leukemic blasts in the bone marrow and peripheral blood. The epigenetic reader BRD4 and its downstream effector MYC have recently been identified as potential drug targets in human AML and ALL. We compared anti‐leukemic efficacies of the small‐molecule BET inhibitor JQ1 and the recently developed BRD4 degraders dBET1 and dBET6 in AML and ALL cells. JQ1, dBET1, and dBET6 were found to suppress growth and viability in all AML and ALL cell lines examined as well as in primary patient‐derived AML and ALL cells, including CD34+/CD38− and CD34+/CD38+ leukemic stem and progenitor cells, independent of the type (variant) of leukemia or molecular driver expressed in leukemic cells. Moreover, we found that dBET6 overcomes osteoblast‐induced drug resistance in AML and ALL cells, regardless of the type of leukemia or the drug applied. Most promising cooperative or even synergistic drug combination effects were seen with dBET6 and the FLT3 ITD blocker gilteritinib in FLT3 ITD‐mutated AML cells, and with dBET6 and the multi‐kinase blocker ponatinib in BCR::ABL1+ ALL cells. Finally, all BRD4‐targeting drugs suppressed interferon‐gamma‐ and tumor necrosis factor‐alpha‐induced expression of the resistance‐related checkpoint antigen PD‐L1 in AML and ALL cells, including LSC. In all assays examined, the BRD4 degrader dBET6 was a superior anti‐leukemic drug compared with dBET1 and JQ1. Together, BRD4 degraders may provide enhanced inhibition of multiple mechanisms of therapy resistance in AML and ALL.