For the efficient degradation of organic pollutants with the goal of reducing the water environment pollution, we employed an alkaline hydrothermal treatment on primeval g-CN to synthesize a hydroxyl-grafted g-CN (CN-0.5) material, from which we engineered a novel Fenton-like catalyst, known as Cu-CN-0.5. The introduction of numerous hydroxyl functional groups allowed the CN-0.5 substrate to stably fix active copper oxide particles through surface complexation, resulting in a low Cu leaching rate during a Cu-CN-0.5 Fenton-like process. A sequence of characterization techniques and theoretical calculations uncovered that interfacial complexation induced charge redistribution on the Cu-CN-0.5 surface. Specifically, some of the π electrons in the tris-s-triazine units were transferred to the copper oxide particles along the newly formed chemical bonds (C-O-Cu), forming a π-deficient area on the tris-s-triazine plane near the complexation site. In a typical Cu-CN-0.5 Fenton-like process, a stable π-π interaction was established due to the favorable positive-negative match of electrostatic potential between the aromatic pollutants and π-deficient areas, leading to a significant improvement in Cu-CN-0.5's adsorption capacity for aromatic pollutants. Furthermore, pollutants also delivered electrons to the Cu-CN-0.5 Fenton-like system via a "through-space" approach, which suppressed the futile oxidation of HO in reducing the high-valent Cu and significantly improved the generation efficiency of OH with high oxidative capacity. As expected, Cu-CN-0.5 not only exhibited an efficient Fenton degradation for several typical aromatic organic pollutants, but also demonstrated both a low metal leaching rate (0.12 mg/L) and a HO utilization rate exceeding 80%. The distinctive Fenton degradation mechanism substantiated the potential of the as-prepared material for effective wastewater treatment applications.