Summary Fluorescence loss in photobleaching experiments and analysis of mitochondrial function using superoxide and redox potential biosensors revealed that mitochondria within individual yeast cells are physically and functionally distinct. Mitochondria that are retained in mother cells during yeast cell division have a significantly more oxidizing redox potential and higher superoxide levels compared to mitochondria in buds. Retention of mitochondria with more oxidizing redox potential in mother cells occurs to the same extent in young and older cells and can account for the age‐associated decline in total cellular mitochondrial redox potential in yeast as they age from 0 to 5 generations. Deletion of Mmr1p, a member of the DSL1 family of tethering proteins that localizes to mitochondria at the bud tip and is required for normal mitochondrial inheritance, produces defects in mitochondrial quality control and heterogeneity in replicative lifespan (RLS). Long‐lived mmr1Δ cells exhibit prolonged RLS, reduced mean generation times, more reducing mitochondrial redox potential and lower mitochondrial superoxide levels compared to wild‐type cells. Short‐lived mmr1Δ cells exhibit the opposite phenotypes. Moreover, short‐lived cells give rise exclusively to short‐lived cells, while the majority of daughters of long‐lived cells are long lived. These findings support the model that the mitochondrial inheritance machinery promotes retention of lower‐functioning mitochondria in mother cells and that this process contributes to both mother–daughter age asymmetry and age‐associated declines in cellular fitness.