Charge transport through single molecules can be influenced by the charge and spin states of redox-active metal centres placed in the transport pathway. These intrinsic properties are usually manipulated by varying the molecule's electrochemical and magnetic environment, a procedure that requires complex setups with multiple terminals. Here we show that oxidation and reduction of organometallic compounds containing either Fe, Ru or Mo centres can solely be triggered by the electric field applied to a two-terminal molecular junction. Whereas all compounds exhibit bias-dependent hysteresis, the Mo-containing compound additionally shows an abrupt voltage-induced conductance switching, yielding high-to-low current ratios exceeding 1,000 at bias voltages of less than 1.0 V. Density functional theory calculations identify a localized, redox-active molecular orbital that is weakly coupled to the electrodes and closely aligned with the Fermi energy of the leads because of the spin-polarized ground state unique to the Mo centre. This situation provides an additional slow and incoherent hopping channel for transport, triggering a transient charging effect in the entire molecule with a strong hysteresis and large high-to-low current ratios.