It is becoming clear that interconnected functional gene networks, rather than individual genes, govern stem cell self-renewal and differentiation. To identify epigenetic factors that impact on human epidermal stem cells we performed siRNA-based genetic screens for 332 chromatin modifiers. We developed a Bayesian mixture model to predict putative functional interactions between epigenetic modifiers that regulate differentiation. We discovered a network of genetic interactions involving EZH2, UHRF1 (both known to regulate epidermal self-renewal), ING5 (a MORF complex component), BPTF and SMARCA5 (NURF complex components). Genome-wide localization and global mRNA expression analysis revealed that these factors impact two distinct but functionally related gene sets, including integrin extracellular matrix receptors that mediate anchorage of epidermal stem cells to their niche. Using a competitive epidermal reconstitution assay we confirmed that ING5, BPTF, SMARCA5, EZH2 and UHRF1 control differentiation under physiological conditions. Thus, regulation of distinct gene expression programs through the interplay between diverse epigenetic strategies protects epidermal stem cells from differentiation.