Memristive switching serves as the basis for a new generation of electronic devices. Conventional memristors are two-terminal devices in which the current is turned on and off by redistributing point defects, e.g., vacancies. Memristors based on alternative mechanisms have been explored, but achieving both high on/off ratio and low switching energy, as needed in applications, remains a challenge. This study reports memristive switching in La0.7Ca0.3MnO3/PrBa2Cu3O7 bilayers with an on/off ratio greater than 103 and results of density functional theory calculations in terms of which it is concluded that the phenomenon is likely the result of a new type of interfacial magnetoelectricity. More specifically, this study shows that an external electric field induces subtle displacements of the interfacial Mn ions, which switches on/off an interfacial magnetic “dead layer”, resulting in memristive behavior for spin-polarized electron transport across the bilayer. The interfacial nature of the switching entails low energy cost, about of a tenth of atto Joule for writing/erasing a “bit”. The results indicate new opportunities for manganite/cuprate systems and other transition metal oxide junctions in memristive applications.