Phenomena that are highly sensitive to magnetic fields can be exploited in sensors and non-volatile memories(1). The scaling of such phenomena down to the single-molecule level(2,3) may enable novel spintronic devices(4). Here, we report magnetoresistance in a single-molecule junction arising from negative differential resistance that shifts in a magnetic field at a rate two orders of magnitude larger than Zeeman shifts. This sensitivity to the magnetic field produces two voltage-tunable forms of magnetoresistance, which can be selected via the applied bias. The negative differential resistance is caused by transient charging(5-7) of an iron phthalocyanine (FePc) molecule on a single layer of copper nitride (Cu2N) on a Cu(001) surface, and occurs at voltages corresponding to the alignment of sharp resonances in the filled and empty molecular states with the Cu(001) Fermi energy. An asymmetric voltage-divider effect enhances the apparent voltage shift of the negative differential resistance with magnetic field, which inherently is on the scale of the Zeeman energy(8). These results illustrate the impact that asymmetric coupling to metallic electrodes can have on transport through molecules, and highlight how this coupling can be used to develop molecular spintronic applications.