Oxaliplatin, satraplatin, and picoplatin are cisplatin analogs that interact with DNA forming intrastrand and interstrand DNA cross-links (ICLs). Replicative bypass of cisplatin DNA adducts requires the cooperative actions of at least three translesion DNA synthesis (TLS) polymerases: Polη, REV1, and Polζ. Because oxaliplatin, satraplatin, and picoplatin contain bulkier chemical groups attached to the platinum core compared with cisplatin, we hypothesized that these chemical additions may impede replicative bypass by TLS polymerases and reduce tolerance to platinum-containing adducts. We examined multiple responses of cancer cells to oxaliplatin, satraplatin, or picoplatin treatment under conditions where expression of a TLS polymerase was limited. Our studies revealed that, although Polη contributes to the tolerance of cisplatin adducts, it plays a lesser role in promoting replication through oxaliplatin, satraplatin, and picoplatin adducts. REV1 and Polζ were necessary for tolerance to all four platinum analogs and prevention of hyperactivation of the DNA damage response after treatment. In addition, REV1 and Polζ were important for the resolution of DNA double-stranded breaks created during replication-associated repair of platinum-containing ICLs. Consistent with ICLs being the predominant cytotoxic lesion, depletion of REV1 or Polζ rendered two different model cell systems extremely sensitive to all four drugs, whereas Polη depletion had little effect. Together, our data suggest that REV1 and Polζ are critical for promoting resistance to all four clinically relevant platinum-based drugs by promoting both translesion DNA synthesis and DNA repair.