DNA interstrand cross-links (ICLs) are repaired in S phase by a complex, multistep mechanism involving translesion DNA polymerases. After replication forks collide with an ICL, the leading strand approaches to within one nucleotide of the ICL ("approach"), a nucleotide is inserted across from the unhooked lesion ("insertion"), and the leading strand is extended beyond the lesion ("extension"). How DNA polymerases bypass the ICL is incompletely understood. Here, we use repair of a site-specific ICL in Xenopus egg extracts to study the mechanism of lesion bypass. Deep sequencing of ICL repair products showed that the approach and extension steps are largely error-free. However, a short mutagenic tract is introduced in the vicinity of the lesion, with a maximum mutation frequency of ~1%. Our data further suggest that approach is performed by a replicative polymerase, while extension involves a complex of Rev1 and DNA polymerase ζ. Rev1-pol ζ recruitment requires the Fanconi anemia core complex but not FancI-FancD2. Our results begin to illuminate how lesion bypass is integrated with chromosomal DNA replication to limit ICL repair-associated mutagenesis.