Mutations fuel evolution while also causing diseases like cancer. Epigenome-targeted DNA repair can help organisms protect important genomic regions from mutation. However, the adaptive value, mechanistic diversity, and evolution of epigenome-targeted DNA repair systems across the tree of life remain unresolved. Here, we investigated the evolution of histone reader domains fused to the DNA repair protein MSH6 (MutS Homolog 6) across over 4,000 eukaryotes. We uncovered a paradigmatic example of convergent evolution: MSH6 has independently acquired distinct histone reader domains, each targeting histone modifications in active genes. Conservation in MSH6 histone reader domains shows signatures of natural selection, particularly for amino acids that bind specific histone modifications. Species that have gained or retained MSH6 histone readers tend to have larger genome sizes, especially marked by a significantly greater contribution of introns to genic regions. These patterns support theoretical predictions about the conditions under which coding sequence hypomutation is likely beneficial. The evolution of epigenome-targeted DNA repair has implications for genome evolution, health, and the mutational origins of genomic diversity across the tree of life.