The rising concerns about global warming and imbalance in the carbon cycle urge rapid development of efficient CO₂ conversion processes. We report an exceptionally productive process for the synthesis of methanol via continuous catalytic hydrogenation of CO₂ under high-pressure conditions (up to 360 bar) over co-precipitated Cu/ZnO/Al₂O₃ catalysts. Outstanding one-pass CO₂ conversion (>95%) and methanol selectivity (>98%) were achieved under an optimized range of reaction conditions. At a very high GHSV of 182,000 h^-1 over a commercial methanol synthesis catalyst, the process delivers 7.7 g_MeOH g^-1_cat h^-1, which is by far the highest yield value reported to date, at the expense of lowered CO₂ conversion (65.8%) and methanol selectivity (77.3%). Using a mixed bed consisting of the Cu/ZnO/Al₂O₃ and H-ZSM-5 catalysts, one-step conversion of CO₂ into dimethyl ether with remarkable selectivity (89%) was attained at the equivalent or higher CO₂ conversion level. Furthermore, we demonstrate that the effluent stream of methanol, rich in H₂ and water, from the methanol synthesis reactor can be directly fed to a reactor containing the H-ZSM-5 catalyst for selective production of alkane (85%) or alkene (42%), depending on the operating pressure of the secondary reactor.