Mammals' longevity is inversely related to mass-specific basal metabolic rate because the generation of reactive oxygen species constrains lifespan. Longevity increases with body mass because the latter is inversely related to mass-specific basal metabolic rates. In placental mammals the longevity residuals from the power laws that describe longevity as a function of mass-specific basal metabolic rates, or body mass, are positively correlated with the relative rates of evolution of cytochrome b, a generator of reactive oxygen species. Therefore, longevity is more accurately described as a function of both mass-specific basal metabolic rate and the relative rate of cytochrome b evolution. The longevity residuals from the power law that describe longevity as a function of body mass are positively correlated with the relative rate of evolution of most other mtDNA-coded proteins. In taxa with very high rate of cytochrome b evolution exceptional longevity is associated with an increase, rather than the predicted decrease, of basal metabolic rates. These finding are compatible with the hypothesis that, in placental mammals, the accelerated evolution of mtDNA-coded proteins, allowed the extension of lifespan by selecting mutations that reduce the generation of reactive oxygen species, mostly by increasing internal proton leak, that accelerates mitochondrial electron transport.