Perpendicular magnetic anisotropy (PMA) has recently been shown to emerge at interfaces of 3d and 5d transition-metal oxides (TMOs). However, strategies to systematically stabilize such interface-driven PMA still remains elusive, hindering further applications of this design approach. Here, tuning crystal symmetry is shown to be an effective means to engineer this interfacial phenomenon. The evolution of PMA strength as a function of ferromagnetic oxide thickness quantitatively reveals the competition between volume- and interface-specific contributions that determine the magnetic anisotropy. By applying different degrees of epitaxial strain, the relative contributions to PMA are modulated, clearly revealing their correlations with crystal symmetries. To be more specific, the volume anisotropy energy is found to be correlated with the tetragonal distortion of the ferromagnetic layer, while the interface anisotropy energy is mainly modulated by the octahedral tilting at the interface. With these insights, superlattices with enhanced interface-driven PMA and higher Curie temperature are realized. These findings reveal a route to engineering interface-driven PMA and associated magnetic phenomena in TMO heterostructures for future spintronic applications.