Somatic missense mutations in histone genes turn these essential proteins into oncohistones, which can drive oncogenesis. Understanding how missense mutations alter histone function is challenging in mammals as the changes occur in a single histone gene. For example, described oncohistone mutations predominantly occur in the histone H3.3 gene, despite the human genome encoding 15 H3 genes. To understand how oncogenic histone missense mutations alter histone function, we leverage the budding yeast model, which encodes only two H3 genes, to explore the functional consequences of oncohistones H3K36M, H3G34W, H3G34L, H3G34R, and H3G34V. An analysis of cells that express each of these variants as the sole copy of H3 reveals that H3K36-mutants show different drug sensitivities compared to H3G34 mutants. This finding suggests that changes to proximal amino acids in the H3 N-terminal tail alter distinct biological pathways. We exploited the caffeine sensitive growth of H3K36 mutant cells to perform a high copy suppressor screen. This screen identified genes linked to histone function and transcriptional regulation, the histone H4/H2A acetyltransferase, Esa1, a forkhead-associated domain-containing gene expression regulator, Tos4, an m6A RNA binding protein, Pho92, and a cyclin-dependent kinase, Sgv1/Bur1. We show that the Esa1 lysine acetyltransferase activity is critical for suppression of the caffeine sensitive growth of H3K36R mutant cells while neither of the characterized binding interactions of Tos4 nor Pho92 are required for suppression. Finally, Sgv1/Bur1-mediated suppression may occur through a dominant negative mechanism. This screen identifies pathways that could be altered by oncohistone mutations and highlights the value of yeast genetics to identify pathways altered by such mutations.