Continuous cancer growth is driven by subsets of self-renewing malignant cells. Targeting of uncontrolled self-renewal through inhibition of stem cell-related signaling pathways has proven challenging. Here, we show that cancer cells can be selectively deprived of self-renewal ability by interfering with their epigenetic state. Re-expression of histone H1.0, a tumor-suppressive factor that inhibits cancer cell self-renewal in many cancer types, can be broadly induced by the clinically well-tolerated compound Quisinostat. Through H1.0, Quisinostat inhibits cancer cell self-renewal and halts tumor maintenance without affecting normal stem cell function. Quisinostat also hinders expansion of cells surviving targeted therapy, independently of the cancer types and the resistance mechanism, and inhibits disease relapse in mouse models of lung cancer. Our results identify H1.0 as a major mediator of Quisinostat's antitumor effect and suggest that sequential administration of targeted therapy and Quisinostat may be a broadly applicable strategy to induce a prolonged response in patients.