To capitalize the improved electrical contact feature, a self-supported hybrid binary/ternary copper and zinc oxides (i.e., ZnO–Cu2O and Cu2O–ZnO–CuO) nanostructures have been generated via a simple potentiostatic mode of anodaization on alpha brass in an alkaline medium. The catalyst nanostructuring i.e., wheat-grain-like to nanograss type structure has improved the mass transport, sluggish kinetics of methanol electrooxidation reaction process, and hindered the competitive oxygen evolution reaction (OER) of direct methanol fuel cell. The catalytic poisoning phenomenon has not been noticed due to two different reaction processes in two potential regions. Interestingly, a significant reduction in overpotential (η10mAcm−2OER−CH3OH) has been noticed for S125@A1 and S125@A2 samples i.e., 236 mV and 350 mV, respectively. The enhancement of current density has been explained through inductive circuit perspective. So, the present study provides a better insights to design and utilize non-precious metal/alloy based catalyst with hindered OER and enhanced methanol electrooxidation reaction activity.