We present a combination of comprehensive experimental and theoretical evidence to unravel the mechanism of two-electron oxygen reduction reaction (ORR) on a catalyst composed of mildly reduced graphene oxide supported on P50 carbon paper (mrGO/P50). This catalyst is unique in that it shows > 99% selectivity towards H2O2, the highest mass activity to date, and essentially zero overpotential in base. Furthermore, the mrGO catalytically active site is unambiguously identified and presents a unique opportunity to investigate mechanisms of carbon-based catalysis in atomistic detail. A wide range of experiments at varying pH is reported; ORR onset potential, Tafel slopes, H/D kinetic isotope effects and O2 reaction order. With DFT reaction energies and known thermodynamic parameters, we calculate the potential and pH dependent free energies of all possible intermediates in this ORR and propose simple kinetic models that give semi-quantitative agreement with all experiments. Our results show that mrGO is semiconducting and cannot support the conventional mechanism of coherently coupled proton-electron transfers. The conducting P50 provides electrons for initiating the ORR via outer-sphere electron transfer to O2(aq), while the semiconducting mrGO provides the active catalytic sites for adsorption of O2-(aq) or HO2(aq), depending upon electrolyte pH. Due to this unique synergistic effect, we describe the mrGO/P50 as a co-catalyst. This concept implies departure from the traditional picture of pre-dicting catalytic activity trends based on a single descriptor, and the co-catalyst design strategy may generally enable other semi-conductors to function as electrocatalysts as well.