The conserved TOR (target of rapamycin) kinase is part of a TORC1 complex that regulates cellular responses to environmental stress, such as amino acid starvation and hypoxia. Dysregulation of Akt-TOR signaling has also been linked to the genesis of cancer, and thus, this pathway presents potential targets for cancer chemotherapeutics. Here we report that rapamycin-sensitive TORC1 signaling is required for the S-phase progression and viability of yeast cells in response to genotoxic stress. In the presence of the DNA-damaging agent methyl methanesulfonate (MMS), TOR-dependent cell survival required a functional S-phase checkpoint. Rapamycin inhibition of TORC1 signaling suppressed the Rad53 checkpoint-mediated induction of ribonucleotide reductase subunits Rnr1 and Rnr3, thereby abrogating MMS-induced mutagenesis and enhancing cell lethality. Moreover, cells deleted for RNR3 were hypersensitive to rapamycin plus MMS, providing the first demonstration that Rnr3 contributes to the survival of cells exposed to DNA damage. Our findings support a model whereby TORC1 acts as a survival pathway in response to genotoxic stress by maintaining the deoxynucleoside triphosphate pools necessary for error-prone translesion DNA polymerases. Thus, TOR-dependent cell survival in response to DNA-damaging agents coincides with increased mutation rates, which may contribute to the acquisition of chemotherapeutic drug resistance.