Rechargeable zinc-air batteries are underpinned by high-performance and durable bifunctional oxygen electrocatalysts. Among the platinum-group metals (PGMs)-free catalysts, the redox-active cobalt-nitrogen-carbon (Co/CoOx–N–C) based materials are promising, however require further structural improvements. This work utilises extremely porous graphene networks (EGO) of hierarchical porosity to in-situ grow ZIF-67 nanocrystals extensively and homogeneously within the porous structure. A simple carbonization of nanoZIF-67@EGO not only generates finely dispersed redox capable Co/CoOx–N–C active sites with the help of residual oxygen functional groups of EGO, but also produces 2-3 dimensional hierarchical porous and conducting structure, readily facilitating high electrochemical surface area. This characteristic structure synergistically contributes to rapid charge and mass transfer rates along with high activity and stability for both ORR and OER. Here, it is worth mentioning that to produce equivalent catalyst material involving different graphitic or template supports requires prolonged and multi-step synthesis routes. The optimized catalyst delivers low potential difference of 0.86 V for bifucntional activity by offering superb ORR half-wave potential of 0.83 V vs RHE and limiting current density of 5.85 mA cm−2 in 0.1 M KOH electrolyte. Zinc-air battery exhibits peak power density of ∼175 mW cm−2 and specific capacity of ∼767 mAh g−1, along with durable cycling round trip efficiency of >63 % (correspond to low voltage gap of ∼0.74 V). These characteristics are better than numerous M–N–C based catalysts reported in the literature. This new strategy holds a great potential to boost the development of diverse MOFs and carbon-based electrocatalysts for a wide range of energy storage and conversion technologies.