In this work, we show an effective strategy combining experimental and computational methods to explore and clarify rational design approaches utilizing transition metals for enhanced electrocatalysis of oxygen reactions. We report a bifunctional electrocatalyst synthesized by a chemical deposition of palladium (Pd) nanoparticles on three-dimensionally ordered mesoporous cobalt oxide (Pd@3DOM-Co3O4) demonstrating extreme stability and activity towards electrocatalytic oxygen reduction and evolution reactions (ORR and OER). Pd@3DOM-Co3O4 exhibits a significantly positive-shifted ORR half-wave potential of 0.88 V (vs. RHE) and a higher OER current density of 41.3 mA cm(-2) measured at 2.0 V (vs. RHE) relative to non-deposited 3DOM-Co3O4. Moreover, in terms of durability, Pd@3DOM-Co3O4 demonstrates a negligible half-wave potential loss with 99.5% retention during ORR and a high current density retention of 96.4% during OER after 1000 cycles of accelerated degradation testing (ADT). Ab-initio computational simulation of the oxygen reactions reveals that the modification of the electronic structure by combining Pd and Co3O4 lowers the Pd d-band center and enhances the electron abundance at the Fermi level, resulting in improved kinetics and conductivity. Furthermore, it is elucidated that the enhanced electrochemical stability is attributed to an elevated carbon corrosion potential (U-corr,U-C) for the Pd@3DOM-Co3O4 surface and an increased dissolution potential (U-diss) of Pd nanoparticles. Meanwhile, synergistic improvements in the bifunctional activity resulting from the combination of Pd and 3DOM-Co3O4 were confirmed by both electrochemical and physical characterization methods, which highlights the practical viability of Pd@3DOM-Co3O4 as an efficient bifunctional catalyst for rechargeable metal-air batteries.