In Saccharomyces cerevisiae, DNA replication stress activates the replication checkpoint, which slows S-phase progression, stabilizes slowed or stalled replication forks, and relieves inhibition of the ribonucleotide reductase (RNR) complex. To identify novel genes that promote cellular viability after replication stress, the S. cerevisiae non-essential haploid gene deletion set (4812 strains) was screened for sensitivity to the RNR inhibitor hydroxyurea (HU). Strains bearing deletions in either CCR4 or CAF1/POP2, which encode components of the cytoplasmic mRNA deadenylase complex, were particularly sensitive to HU. We found that Ccr4 cooperated with the Dun1 branch of the replication checkpoint, such that ccr4Delta dun1Delta strains exhibited irreversible hypersensitivity to HU and persistent activation of Rad53. Moreover, because ccr4Delta and chk1Delta exhibited epistasis in several genetic contexts, we infer that Ccr4 and Chk1 act in the same pathway to overcome replication stress. A counterscreen for suppressors of ccr4Delta HU sensitivity uncovered mutations in CRT1, which encodes the transcriptional repressor of the DNA-damage-induced gene regulon. Whereas Dun1 is known to inhibit Crt1 repressor activity, we found that Ccr4 regulates CRT1 mRNA poly(A) tail length and may subtly influence Crt1 protein abundance. Simultaneous overexpression of RNR2, RNR3 and RNR4 partially rescued the HU hypersensitivity of a ccr4Delta dun1Delta strain, consistent with the notion that the RNR genes are key targets of Crt1. These results implicate the coordinated regulation of Crt1 via Ccr4 and Dun1 as a crucial nodal point in the response to DNA replication stress.