The highly conserved molecular chaperones Hsp90 and Hsp70 are indispensible for folding and maturation of a significant fraction of the proteome, including many proteins involved in signal transduction and stress response. To examine the dynamics of chaperone-client interactions after DNA damage, we applied quantitative affinity-purification mass spectrometry (AP-MS) proteomics to characterize interactomes of the yeast Hsp70 isoform Ssa1 and Hsp90 isoform Hsp82 before and after exposure to methyl methanesulfonate (MMS). Of 256 proteins identified and quantified via 16O/18O labeling and LC-MS/MS, 142 are novel Hsp70/90 interactors. Nearly all interactions remained unchanged or decreased after DNA damage, but 5 proteins increased interactions with Ssa1 and/or Hsp82, including the ribonucleotide reductase (RNR) subunit Rnr4. Inhibiting Hsp70 or 90 chaperone activity destabilized Rnr4 in yeast and its vertebrate homolog hRMM2 in breast cancer cells. In turn, pre-treatment of cancer cells with chaperone inhibitors sensitized cells to the RNR inhibitor gemcitabine, suggesting a novel chemotherapy strategy.