We have fabricated a unique memristive device by molecular engineering and demonstrated that the leakage current tuning in the device is 100 times more efficient than that in a standard device. Molecular analogs of the memristive matrices used here are an electrochemically active conjugated Co(III) polymer (CP) and a nonconjugated Co(III) polymer (NCP), which have been synthesized in good yield and characterized by H-1 NMR spectroscopy. Redox switching of an organic-metallic hybrid polymer generates bistable states with a large ON/OFF ratio that supports random flip-flops for several hours. Thus, we provide a synthetic solution to leakage current restriction, one of the fundamental problems faced when fabricating state-of-the-art electronic devices.