Abstract In Saccharomyces cerevisiae, histone H3 lysine 56 acetylation (H3K56Ac) is present in newly synthesized histones deposited throughout the genome during DNA replication. The sirtuins Hst3 and Hst4 deacetylate H3K56 after S phase, and virtually all histone H3 molecules are K56 acetylated throughout the cell cycle in hst3∆ hst4∆ mutants. Failure to deacetylate H3K56 causes thermosensitivity, spontaneous DNA damage, and sensitivity to replicative stress via molecular mechanisms that remain unclear. Here we demonstrate that unlike wild-type cells, hst3∆ hst4∆ cells are unable to complete genome duplication and accumulate persistent foci containing the homologous recombination protein Rad52 after exposure to genotoxic drugs during S phase. In response to replicative stress, cells lacking Hst3 and Hst4 also displayed intense foci containing the Rfa1 subunit of the single-stranded DNA binding protein complex RPA, as well as persistent activation of DNA damage–induced kinases. To investigate the basis of these phenotypes, we identified histone point mutations that modulate the temperature and genotoxic drug sensitivity of hst3∆ hst4∆ cells. We found that reducing the levels of histone H4 lysine 16 acetylation or H3 lysine 79 methylation partially suppresses these sensitivities and reduces spontaneous and genotoxin-induced activation of the DNA damage-response kinase Rad53 in hst3∆ hst4∆ cells. Our data further suggest that elevated DNA damage–induced signaling significantly contributes to the phenotypes of hst3∆ hst4∆ cells. Overall, these results outline a novel interplay between H3K56Ac, H3K79 methylation, and H4K16 acetylation in the cellular response to DNA damage.