Establishing genetic and chemo-genetic interactions has played key roles in elucidating mechanisms by which certain chemicals perturb cellular functions. In contrast to gene disruption/depletion strategies to identify mechanisms of drug resistance, searching for point-mutational genetic suppressors that can identify separation- or gain-of-function mutations has been limited. Here, by demonstrating its utility in identifying chemical-genetic suppressors of sensitivity to the DNA topoisomerase I poison camptothecin or the poly(ADP-ribose) polymerase inhibitor olaparib, we detail an approach allowing systematic, large-scale detection of spontaneous or chemically-induced suppressor mutations in yeast or haploid mammalian cells in a short timeframe, and with potential applications in other haploid systems. In addition to applications in molecular biology research, this protocol can be used to identify drug targets and predict drug-resistance mechanisms. Mapping suppressor mutations on the primary or tertiary structures of protein suppressor hits provides insights into functionally relevant protein domains. Importantly, we show that olaparib resistance is linked to missense mutations in the DNA binding regions of PARP1, but not in its catalytic domain. This provides experimental support to the concept of PARP1 trapping on DNA as the prime source of toxicity to PARP inhibitors, and points to a novel olaparib resistance mechanism with potential therapeutic implications.