Epigenetic histone trimethylation on lysine 9 (H3K9me3) represents a major molecular signal for genome stability and gene silencing conserved from worms to man. However, the functional role of the H3K9 trimethylases SUV39H1/2 in mammalian tissue homeostasis remains largely unknown. Here, we use a spontaneous dog model with monogenic inheritance of a recessive SUV39H2 loss-of-function variant and impaired differentiation in the epidermis, a self-renewing tissue fueled by stem and progenitor cell proliferation and differentiation. Our results demonstrate that SUV39H2 maintains the stem and progenitor cell pool by restricting fate conversion through H3K9me3 repressive marks on gene promoters encoding components of the Wnt/p63/adhesion axis. When SUV39H2 function is lost, repression is relieved, and enhanced Wnt activity causes progenitor cells to prematurely exit the cell cycle, a process mimicked by pharmacological Wnt activation in primary canine, human, and mouse keratinocytes. As a consequence, the stem cell growth potential of cultured SUV39H2-deficient canine keratinocytes is exhausted while epidermal differentiation and genome stability are compromised. Collectively, our data identify SUV39H2 and potentially also SUV39H1 as major gatekeepers in the delicate balance of progenitor fate conversion through H3K9me3 rate-limiting road blocks in basal layer keratinocytes.