Mitochondrial genomes (mtDNA) encode essential subunits of the mitochondrial respiratory chain. Mutations in mtDNA can cause a shortage in cellular energy supply, which can lead to numerous mitochondrial diseases. How cells secure mtDNA integrity over generations has remained unanswered. Here, we show that the single-celled yeast Saccharomyces cerevisiae can intracellularly distinguish between functional and defective mtDNA and promote generation of daughter cells with increasingly healthy mtDNA content. Purifying selection for functional mtDNA occurs in a continuous mitochondrial network and does not require mitochondrial fission but necessitates stable mitochondrial subdomains that depend on intact cristae morphology. Our findings support a model in which cristae-dependent proximity between mtDNA and the proteins it encodes creates a spatial “sphere of influence,” which links a lack of functional fitness to clearance of defective mtDNA.