The RAD6/RAD18 pathway of DNA damage tolerance overcomes unrepaired lesions that block replication forks. It is subdivided into two branches: translesion DNA synthesis, which is frequently error prone, and the error-free DNA-damage-avoidance subpathway. Here, we show that Rad5(HLTF/SHPRH), which mediates the error-free branch, has a major role in the response to DNA damage caused by methyl methanesulfonate (MMS) during chromosome replication, whereas translesion synthesis polymerases make only a minor contribution. Both the ubiquitin-ligase and the ATPase/helicase activities of Rad5 are necessary for this cellular response. We show that Rad5 is required for the progression of replication forks through MMS-damaged DNA. Moreover, supporting its role during replication, this protein reaches maximum levels during S phase and forms subnuclear foci when replication occurs in the presence of DNA damage. Thus, Rad5 ensures the completion of chromosome replication under DNA-damaging conditions while minimizing the risk of mutagenesis, thereby contributing significantly to genome integrity maintenance.