A small heat of reaction limits the efficiency of the catalytic hydrogenation of CO2 to form methanol; an improved efficiency can be achieved by shifting the thermodynamic equilibrium toward the formation of methanol. The exothermic adsorption of the products in sorption catalysts is shown to increase the reaction yield. The sorption catalysts consist of catalytically active Cu particles incorporated into a zeolite, which is known to strongly absorb water. In addition to high reaction yield of methanol, the sorption catalyst reduces CO2 to CO and dimethyl ether. An enhancement factor of up to 400% for CO and 130% for methanol and dimethyl ether at a relatively low pressure of 15 bar is shown. Furthermore, the following relevant parameters for future technical realization are derived: a high catalytic activity and the reversible adsorption of the products at reaction conditions. A key experiment that combines a catalytic reaction and a pressure swing desorption is presented and demonstrates the feasibility of sorption-enhanced catalysis for efficient energy use in large-scale reactors.