Mutations in the ATM tumor suppressor gene confer hypersensitivity to DNA-damaging chemotherapeutic agents. To explore genetic resistance mechanisms, we performed genome-wide CRISPR-Cas9 screens in cells treated with the DNA topoisomerase I inhibitor topotecan. Thus, we here establish that inactivating terminal components of the non-homologous end-joining (NHEJ) machinery or of the BRCA1-A complex specifically confer topotecan resistance to ATM-deficient cells. We show that hypersensitivity of ATM-mutant cells to topotecan or the poly-(ADP-ribose) polymerase (PARP) inhibitor olaparib reflects delayed engagement of homologous recombination at DNA-replication-fork associated single-ended double-strand breaks (DSBs), allowing some to be subject to toxic NHEJ. Preventing DSB ligation by NHEJ, or enhancing homologous recombination by BRCA1-A complex disruption, suppresses this toxicity, highlighting a crucial role for ATM in preventing toxic LIG4-mediated chromosome fusions. Notably, suppressor mutations in ATM-mutant backgrounds are different to those in BRCA1-mutant scenarios, suggesting new opportunities for patient stratification and additional therapeutic vulnerabilities for clinical exploitation.