Cu–Ga catalysts are potential candidates for activating the selective and stable hydrogenation of carbon dioxide to methanol and dimethyl ether. This work explores the structure–function relationship in specific Cu–Ga/CeO2–ZrO2 catalysts with different Ga loadings. Combining experiments with density functional theory calculations, we find the most well-balanced Cu–Ga interphase (structure) and promote specific mechanistic pathways of the reaction (function). The experiments yielded the highest selectivity of the desired products when the Cu and Ga amounts were equal. The experimental work and density functional theory calculations demonstrated that methanol is formed through the carboxyl pathway on the Cu catalyst, while Ga promotes the formate pathway. Consequently, the productivities of both methanol and dimethyl ether are enhanced. The experimental results match well with the theoretical calculations. Comparing our results with other Ga-promoting systems, we also prove that Cu achieves better balance than Ni and Co