In this research, the oxidation of a series of benzoins, R-C(=O)-CH(OH)-R, where R = phenyl, 4-methoxyphenyl, 4-bromophenyl, and 2-naphthyl, by hydrogen peroxide in the presence of nanostructured HKUST-1 (suspension in acetonitrile/water mixture) was studied. The respective benzoic acids were the only products of the reactions. The initial average reaction rates were experimentally determined at different concentrations of benzoin, H2O2 and an effective concentration of HKUST-1. The sorption of the isotherms of benzoin, dimethoxybenzoin and benzoic acid on HKUST-1, as well as their sorption kinetic curves, were measured. The increase in H2O2 concentration expectedly led to an acceleration of the reaction. The dependencies of the benzoin oxidation rates on the concentrations of both benzoin and HKUST-1 passed through the maxima. This finding could be explained by a counterplay between the increasing reaction rate and increasing benzoin sorption on the catalyst with the increase in the concentration. The electronic effect of the substituent in benzoin had a significant influence on the reaction rate, while no relation between the size of the substrate molecule and the rate of its oxidation was found. It was confirmed by DFT modeling that the reaction could pass through the Baeyer–Villiger mechanism, involving an attack by the HOO– anion on the C atom of the activated C=O group.