Accelerated rates of mitochondrial protein evolution have been proposed to reflect Darwinian coadaptation for efficient energy production for mammalian flight and brain activity. However, several features of mammalian mtDNA (absence of recombination, small effective population size, and high mutation rate) promote genome degradation through the accumulation of weakly deleterious mutations. Here, we present evidence for "compensatory" adaptive substitutions in nuclear DNA- (nDNA) encoded mitochondrial proteins to prevent fitness decline in primate mitochondrial protein complexes. We show that high mutation rate and small effective population size, key features of primate mitochondrial genomes, can accelerate compensatory adaptive evolution in nDNA-encoded genes. We combine phylogenetic information and the 3D structure of the cytochrome c oxidase (COX) complex to test for accelerated compensatory changes among interacting sites. Physical interactions among mtDNA- and nDNA-encoded components are critical in COX evolution; amino acids in close physical proximity in the 3D structure show a strong tendency for correlated evolution among lineages. Only nuclear-encoded components of COX show evidence for positive selection and adaptive nDNA-encoded changes tend to follow mtDNA-encoded amino acid changes at nearby sites in the 3D structure. This bias in the temporal order of substitutions supports compensatory weak selection as a major factor in accelerated primate COX evolution.