Reduced activity of two genes in combination often has a more detrimental effect than expected. Such epistatic interactions not only occur when genes are mutated but also due to variation in gene expression, including among isogenic individuals in a controlled environment. We hypothesized that these 'epigenetic' epistatic interactions could place important constraints on the evolution of gene expression. Consistent with this, we show here that yeast genes with many epistatic interaction partners typically show low expression variation among isogenic individuals and low variation across different conditions. In addition, their expression tends to remain stable in response to the accumulation of mutations and only diverges slowly between strains and species. Yeast promoter architectures, the retention of gene duplicates, and the divergence of expression between humans and chimps are also consistent with selective pressure to reduce the likelihood of harmful epigenetic epistatic interactions. Based on these and previous analyses, we propose that the tight regulation of epistatic interaction network hubs makes an important contribution to the maintenance of a robust, 'canalized' phenotype. Moreover, that epigenetic epistatic interactions may contribute substantially to fitness defects when single genes are deleted.