Hyperactivation of the MAPK signaling pathway motivates the clinical use of MAPK inhibitors for BRAF-mutant melanomas. Heterogeneity in differentiation state due to epigenetic plasticity, however, results in cell-to-cell variability in the state of MAPK dependency, diminishing the efficacy of MAPK inhibitors. To identify key regulators of such variability, we screen 276 epigenetic-modifying compounds, individually or combined with MAPK inhibitors, across genetically diverse and isogenic populations of melanoma cells. Following single-cell analysis and multivariate modeling, we identify three classes of epigenetic inhibitors that target distinct epigenetic states associated with either one of the lysine-specific histone demethylases Kdm1a or Kdm4b, or BET bromodomain proteins. While melanocytes remain insensitive, the anti-tumor efficacy of each inhibitor is predicted based on melanoma cells' differentiation state and MAPK activity. Our systems pharmacology approach highlights a path toward identifying actionable epigenetic factors that extend the BRAF oncogene addiction paradigm on the basis of tumor cell differentiation state.