We report the preparation and hydrogenation performance of a single-site palladium catalyst that was obtained by the anchoring of Pd atoms into the cavities of mesoporous polymeric graphitic carbon nitride. The characterization of the material confirmed the atomic dispersion of the palladium phase throughout the sample. The catalyst was applied for three-phase hydrogenations of alkynes and nitroarenes in a continuous-flow reactor, showing its high activity and product selectivity in comparison with benchmark catalysts based on nanoparticles. Density functional theory calculations provided fundamental insights into the material structure and attributed the high catalyst activity and selectivity to the facile hydrogen activation and hydrocarbon adsorption on atomically dispersed Pd sites.