Interactions between nuclear and mitochondrial gene products are critical for eukaryotic cell function. Nuclear genes encoding mitochondrial-targeted proteins (N-mt genes) experience elevated rates of evolution, which has often been interpreted as evidence of nuclear compensation in response to elevated mitochondrial mutation rates. However, N-mt genes may be under relaxed functional constraints, which could also explain observed increases in their evolutionary rate. To disentangle these hypotheses, we examined patterns of sequence and structural evolution in nuclear and mitochondrial-encoded oxidative phosphorylation proteins from species in the angiosperm genus Silene with vastly different mitochondrial mutation rates. We found correlated increases in N-mt gene evolution in species with fast-evolving mitochondrial DNA. Structural modeling revealed an overrepresentation of N-mt substitutions at positions that directly contact mutated residues in mitochondrial-encoded proteins, despite overall patterns of conservative structural evolution. These findings support the hypothesis that selection for compensatory changes in response to mitochondrial mutations contributes to the elevated rate of evolution in N-mt genes. We discuss these results in light of theories implicating mitochondrial mutation rates and mitonuclear co-evolution as drivers of speciation and suggest comparative and experimental approaches that could take advantage of heterogeneity in rates of mtDNA evolution across eukaryotes to evaluate such theories.