The hypoxia-inducible factor 1-α (HIF-1α) enables cells to adapt and respond to hypoxia (Hx), and the activity of this transcription factor is regulated by several oncogenic signals and cellular stressors. While the pathways controlling normoxic degradation of HIF-1α are well understood, the mechanisms supporting the sustained stabilization and activity of HIF-1α under Hx are less clear. We report that ABL kinase activity protects HIF-1α from proteasomal degradation during Hx. Using a fluorescence-activated cell sorting (FACS)-based CRISPR/Cas9 screen, we identified HIF-1α as a substrate of the cleavage and polyadenylation specificity factor-1 (CPSF1), an E3-ligase which targets HIF-1α for degradation in the presence of an ABL kinase inhibitor in Hx. We show that ABL kinases phosphorylate and interact with CUL4A, a cullin ring ligase adaptor, and compete with CPSF1 for CUL4A binding, leading to increased HIF-1α protein levels. Further, we identified the MYC proto-oncogene protein as a second CPSF1 substrate and show that active ABL kinase protects MYC from CPSF1-mediated degradation. These studies uncover a role for CPSF1 in cancer pathobiology as an E3-ligase antagonizing the expression of the oncogenic transcription factors, HIF-1α and MYC.