Oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) are essential reactions for energy-storage and -conversion devices relying on oxygen electrochemistry. High-performance, nonprecious metal-based hybrid catalysts are developed from postsynthesis integration of dual-phase spinel MnCo2O4 (dp-MnCo2O4) nanocrystals with nanocarbon materials, e.g., carbon nanotube (CNT) and nitrogen-doped reduced graphene oxide (N-rGO). The synergic covalent coupling between dp-MnCo2O4 and nanocarbons effectively enhances both the bifunctional ORR and OER activities of the spinel/nanocarbon hybrid catalysts. The dp-MnCo2O4/N-rGO hybrid catalysts exhibited comparable ORR activity and superior OER activity compared to commercial 30 wt % platinum supported on carbon black (Pt/C). An electrically rechargeable zinc-air battery using dp-MnCo2O4/CNT hybrid catalysts on the cathode was successfully operated for 64 discharge-charge cycles (or 768 h equivalent), significantly outperforming the Pt/C counterpart, which could only survive up to 108 h under similar conditions.