The efficient electrochemical conversion and storage devices can be boosted by the development of cost-effective and durable electrocatalysts. However, simultaneous in-depth understanding of the reaction mechanism is also required. Herein, we report the preparation, characterization, and electrochemical activities of bimetallic NixCo1-x NPs and core-shell NixCo1-x@NixCo1-xO NPs stabilized on N-doped carbon nanotubes (NCNTs). The electrocatalyst is derived from a bimetallic MOF {[Ni0.5Co0.5(bpe)2(N(CN)2)](N(CN)2)·(5H2O)}n (1) via pyrolysis followed by calcination. Pyrolysis of the bimetallic MOF gives rise to bimetallic nanoparticles stabilized on NCNTs, which, when subsequently calcined, leads to the formation of a core-shell structure with a semiconducting oxide shell (NixCo1-xO) encapsulating the NixCo1-x bimetallic NP core. Detailed evaluation of the electrocatalytic performance of NixCo1-x@NixCo1-xO/NCNT proves its worth as a bifunctional catalyst with 380 mV overpotential for oxygen evolution reaction at 10 mA cm-2 current density and 0.87 V (vs RHE) onset for oxygen reduction reaction in the alkaline medium. Additionally, the prepared electrocatalyst efficiently catalyzes the hydrogen evolution reaction with a nominal overpotential of 74 mV (vs RHE) for reaching 10 mA cm-2 current density in acidic medium. The practical applicability of this catalyst is further upheld in the fabrication of a zinc-air battery having high specific capacity with high round-trip efficiency and adequate cycle life. DFT calculations establish that the structure of NixCo1-x@NixCo1-xO/NCNT is crucial for its electrochemical activity since it has the threefold advantages of cooperative charge transfer from Co to Ni, synergistic relationship between the conductive alloy core and semiconducting oxide shell, and a highly conductive N-doped CNT matrix.