Solar energy is the most available renewable resource and has great potential for various applications. Solar heat pumps are limited when operating alone due to weather and the unstable and intermittent nature of solar energy. The idea of combining a solar collector with an air-source heat pump (ASHP) is proposed to solve the problems. Taking solar energy and air energy as the heat source of the system can improve the heat collection efficiency and heating performance coefficient of the dual-supply heating system in realizing the efficient and stable operation of the whole unit. This study investigated the application of a solar–air-source heat pump (S/AS-HP) dual-supply heating system for a residential building in Lhasa and compared the winter work performance and economic benefits of three different heating forms: solar–air-source heat pump, air-source heat pump, and solar–electric auxiliary heating systems. A simulation model was established and analyzed using the measurement data. The results show that during the heating period, the temperature of the primary side water supply is stable at about 60 °C, and the total operating hours of the solar collector period accounted for 26.9% of the total hours, of which 23.16% were independent operating hours. The average COPsys of the solar–air-source heat pump is 4.21, which greatly improves work performance compared with other systems, and the annual cost is the lowest among the three forms for the same service life at 41,824.6 CNY, saving 9.6% and 35.1% per year compared with the air-source heat pump system and the solar–electric auxiliary heating system. Considering conditions in alpine regions, S/AS-HP systems are the optimal heating solution for single buildings.