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High temperature creep deformation of hcp-Mg alloys is dominated by dislocation climb driven by out-of-plane (OOP) vacancy migration. Past experiments and atomistic simulations have indicated that Zn addition reduces vacancy migration tendencies and improves creep resistance. Here, we have compared in-plane (IP) and out-of-plane (OOP) vacancy migration mechanisms in binary Mg–X (Ca, Y, and Gd) and ternary Mg–X (Ca, Y, and Gd)–Zn alloys using density functional theory based first principles computations. Irrespective of Zn addition, the migration barrier for OOP diffusion was consistently higher than IP in our prototype binary and ternary alloys. The presence of Zn in ternary systems, however, substantially increases the OOP activation barrier relative to binary alloys. The higher OOP barrier in Mg–X–Zn was attributed to favorable local relaxation, enhanced charge localization, higher interplanar bond stiffness, and greater s orbital electron occupancy in the peak saddle state. Combined, these factors restrict non-conservative dislocation climb by impeding out-of-plane vacancy movement and improve the creep resistance of ternary Mg–X (Ca, Y, and Gd)–Zn alloys. [ABSTRACT FROM AUTHOR]