In budding yeast, one-ended DNA double-strand breaks (DSBs) and damaged replication forks are repaired by break-induced replication (BIR), a homologous recombination pathway that requires the Pol32 subunit of DNA polymerase delta. DNA replication stress is prevalent in cancer, but BIR has not been characterized in mammals. In a cyclin E overexpression model of DNA replication stress, POLD3, the human ortholog of POL32, was required for cell cycle progression and processive DNA synthesis. Segmental genomic duplications induced by cyclin E overexpression were also dependent on POLD3, as were BIR-mediated recombination events captured with a specialized DSB repair assay. We propose that BIR repairs damaged replication forks in mammals, accounting for the high frequency of genomic duplications in human cancers.