The insertion of a thin amorphous ZnO (a-ZnO) dielectric layer between the Pt electrode and crystallized ZnO (c-ZnO) insulator has been known to enhance magnetic modulation of Ti/c-ZnO/Pt resistive random-access memory (RRAM) devices. This study investigates the relationship between resistivity and magnetization switching within Ti/c-ZnO/a-ZnO/Pt and Ti/c-ZnO/Pt structures. Under an applied electric field, both devices show magnetization changes associated with resistance states, but the Ti/c-ZnO/a-ZnO/Pt RRAM device exhibits substantially enhanced magnetic modulation, improved resistive switching (RS) ratio and reduced operating voltage of the ZnO film. The saturation magnetization of the ZnO film in a low-resistance state is more than ten times higher compared to that in its initial state under a V-SET/V-RESET ratio of 0.52-0.56 V. Furthermore, the Ti/cZnO/a-ZnO/Pt structure shows an improvement in the RS ratio by approximately 880 times, and the coefficients of variation for SET and RESET voltages are only 1.6% and 2.2%, respectively. We propose that these results are related to the stabilized local oxygen vacancy (Vo) migration, metal-like nature of Vo-based filamentary conducting paths and the coupling of Vos with each other among the conductive filaments in the c-ZnO layer. This work presents an efficient means to electrically control the magnetism in metal oxides, i.e., inserting a thin oxide layer (a-ZnO) in electrode-insulator interfaces.