We study a high-TC superconducting (YBa2Cu3O7-d) / ferromagnetic (Co/Pt multilayer) hybrid which exhibits resistance switching driven by the magnetic history: depending on the direction of the external field, a pronounced decrease or increase of the mixed-state resistance is observed as magnetization reversal occurs within the Co/Pt multilayer. We demonstrate that stray magnetic fields cause these effects via i) creation of vortices/antivortices and ii) magnetostatic pinning of vortices that are induced by the external field.