The catalytic performance of zirconium-based metal-organic frameworks (UiO-66, UiO-67, and MOF-801) in cyclohexene oxidation with aqueous hydrogen peroxide can be greatly improved by adding a source of protons directly into the reaction mixture. A blend of Zr-MOF and protons favors heterolytic activation of H2O2 and makes possible selective formation of epoxide and diol with negligible formation of allylic oxidation products. Additives of HClO4 suppress the rates of H2O2 decomposition over Zr-MOF and increase oxidant utilization efficiency. No structural changes occur in the acid-activated Zr-MOF. The catalyst does not suffer metal leaching, reveals a truly heterogeneous nature of the catalysis, and can be recovered and reused.