The DNA repair enzyme polynucleotide kinase/phosphatase (PNKP) protects genome integrity by restoring ligatable 5'-phosphate and 3'-hydroxyl termini at single-strand breaks (SSBs). In humans, PNKP mutations underlie the neurological disease known as MCSZ, but these individuals are not predisposed for cancer, implying effective alternative repair pathways in dividing cells. Homology-directed repair (HDR) of collapsed replication forks was proposed to repair SSBs in PNKP-deficient cells, but the critical HDR protein Rad51 is not required in PNKP-null (pnk1Δ) cells of Schizosaccharomyces pombe. Here, we report that pnk1Δ cells have enhanced requirements for Rad3 (ATR/Mec1) and Chk1 checkpoint kinases, and the multi-BRCT domain protein Brc1 that binds phospho-histone H2A (γH2A) at damaged replication forks. The viability of pnk1Δ cells depends on Mre11 and Ctp1 (CtIP/Sae2) double-strand break (DSB) resection proteins, Rad52 DNA strand annealing protein, Mus81-Eme1 Holliday junction resolvase, and Rqh1 (BLM/WRN/Sgs1) DNA helicase. Coupled with increased sister chromatid recombination and Rad52 repair foci in pnk1Δ cells, these findings indicate that lingering SSBs in pnk1Δ cells trigger Rad51-independent homology-directed repair of collapsed replication forks. From these data, we propose models for HDR-mediated tolerance of persistent SSBs with 3' phosphate in pnk1Δ cells.