A simple cell model consisting of a gene regulatory network with epigenetic feedback regulation is studied to evaluate the effect of epigenetic dynamics on adaptation and evolution. We find that, the type of epigenetic dynamics considered enables a cell to adapt to unfamiliar environmental changes, for which no regulatory program has been prepared, through noise-driven selection of a cellular state with a high growth rate. Furthermore, we demonstrate that the inclusion of epigenetic regulation promotes evolutionary development of a regulatory network that can respond to environmental changes in a fast and precise manner. These results strongly suggest that epigenetic feedback regulation in gene expression dynamics provides a significant increase in fitness by engendering an increase in cellular plasticity during adaptation and evolution.