HIV replication in nondividing host cells occurs in the presence of high concentrations of noncanonical dUTP, apolipoprotein B mRNA-editing, enzyme-catalytic, polypeptide-like 3 (APOBEC3) cytidine deaminases, and SAMHD1 (a cell cycle-regulated dNTP triphosphohydrolase) dNTPase, which maintains low concentrations of canonical dNTPs in these cells. These conditions favor the introduction of marks of DNA damage into viral cDNA, and thereby prime it for processing by DNA repair enzymes. Accessory protein Vpr, found in all primate lentiviruses, and its HIV-2/simian immunodeficiency virus (SIV) SIVsm paralogue Vpx, hijack the CRL4DCAF1 E3 ubiquitin ligase to alleviate some of these conditions, but the extent of their interactions with DNA repair proteins has not been thoroughly characterized. Here, we identify HLTF, a postreplication DNA repair helicase, as a common target of HIV-1/SIVcpz Vpr proteins. We show that HIV-1 Vpr reprograms CRL4DCAF1 E3 to direct HLTF for proteasome-dependent degradation independent from previously reported Vpr interactions with base excision repair enzyme uracil DNA glycosylase (UNG2) and crossover junction endonuclease MUS81, which Vpr also directs for degradation via CRL4DCAF1 E3. Thus, separate functions of HIV-1 Vpr usurp CRL4DCAF1 E3 to remove key enzymes in three DNA repair pathways. In contrast, we find that HIV-2 Vpr is unable to efficiently program HLTF or UNG2 for degradation. Our findings reveal complex interactions between HIV-1 and the DNA repair machinery, suggesting that DNA repair plays important roles in the HIV-1 life cycle. The divergent interactions of HIV-1 and HIV-2 with DNA repair enzymes and SAMHD1 imply that these viruses use different strategies to guard their genomes and facilitate their replication in the host.