Genetic interactions reveal the functional relationships between pairs of genes. In this study, we describe a method for the systematic generation and quantitation of triple mutants, termed triple-mutant analysis (TMA). We have used this approach to interrogate partially redundant pairs of genes in S. cerevisiae, including ASF1 and CAC1, two histone chaperones. After subjecting asf1Δ cac1Δ to TMA, we found that the Swi/Snf Rdh54 protein compensates for the absence of Asf1 and Cac1. Rdh54 more strongly associates with the chromatin apparatus and the pericentromeric region in the double mutant. Moreover, Asf1 is responsible for the synthetic lethality observed in cac1Δ strains lacking the HIRA-like proteins. A similar TMA was carried out after deleting both CLB5 and CLB6, cyclins that regulate DNA replication, revealing a strong functional connection to chromosome segregation. This approach can reveal functional redundancies that cannot be uncovered through traditional double-mutant analyses.