Strategies for decarbonizing residential building energy services can be divided into three categories: (1) shifting to less carbon-intensive fuels in the building energy supply mix, (2) adopting more energy-efficient end-use appliances, and (3) improving the thermal properties of buildings. We develop an optimization model that incorporates all three strategies, and determines the least-cost decarbonization pathway by balancing these levers and leveraging their synergistic relationships. Hourly service demand profiles are established using appliance-level empirical data and the CitySim building energy simulation software. We apply this framework to the residential buildings sector of Austin, Texas, which is a valuable test case due to its ambitious climate policy, rapid population growth, and strong space cooling demand in line with the shift of building energy demand toward warmer regions in the U.S. and globally. Results show that optimal decarbonization relies primarily on the electrification of end-uses and concomitant decarbonization of electricity supply. End-use appliance efficiency plays a comparatively minor role, limited to specific end-uses like lighting, space heating, and water heating. Upgrading building thermal efficiency significantly reduces the cost of climate policy, revealing an important policy complementarity between carbon reduction measures and building energy codes.