Density–functional theory (DFT) calculations that combine a systematic sweep of Hartree–Fock (HF) exchange (0–100%) with on-site Hubbard corrections (+ U) clarify how hybrid DFT+ U resolves the band-gap problem in transition-metal oxides across the correlation-strength spectrum. Using the screened hybrid HSE06 functional, we find that weakly correlated TiO 2 shows an almost linear E g –HF trend and reproduces the experimental gap of 3.20eV with only 2% exact exchange and a modest U Ti = 4 . 0 eV. By contrast, strongly correlated antiferromagnetic NiO exhibits a pronounced kink near 15% HF: beyond this point hybrid exchange alone saturates ( E g ≲ 3 eV), underscoring its inability to capture Mott physics. Introducing U Ni = 6 . 3 eV together with 15% HF restores the full 4.30eV gap, in quantitative agreement with optical and photoemission data. Band-structure and DOS analyses show that the dual correction localises Ni 3 d states and fully separates the lower and upper Hubbard bands, whereas TiO 2 requires only minor conduction-band shifts. These results delineate the respective domains of validity of hybrid exchange and on-site Coulomb terms, provide a transferable workflow for selecting HF+ U parameters, and demonstrate that accurate yet economical band-gap predictions across weakly and strongly correlated oxides demand correlation-strength-dependent calibration of exchange and on-site interactions.