The functional basis of genetic robustness, the ability of organisms to suppress the effects of mutations, remains incompletely understood. We exposed a set of 15 strains of Saccharomyces cerevisiae form diverse environments to increasing doses of the chemical mutagen EMS. The number of the resulting random mutations was similar for all tested strains. However, there were differences in immediate mortality after the mutagenic treatment and in defective growth of survivors. An analysis of gene expression revealed that immediate mortality was lowest in strains with lowest expression of transmembrane proteins, which are rich in thiol groups and thus vulnerable to EMS. A signal of genuine genetic robustness was detected for the other trait, the ability to grow well despite bearing non-lethal mutations. Increased tolerance of such mutations correlated with high expression of genes responsible for the oxidative energy metabolism, suggesting that the negative effect of mutations can be buffered if enough energy is available. We confirmed this finding in three additional tests of the ability to grow on (i) fermentable or non-fermentable sources of carbon, (ii) under chemical inhibition of the electron transport chain and (iii) during overexpression of its key component, cytochrome c. Our results add the capacity to generate energy as a general mechanism of genetic robustness.