This study proposes an efficient, flexible and low-carbon combined heating and power (CHP) system with solar energy and methanol as energy inputs. The system features a modular design combining concentrated photovoltaics, methanol thermochemistry and internal combustion engines that enable efficient power generation, effective energy storage and flexible, demand-driven supply of heat and power. Cascaded utilization of solar energy results in a high net solar-to-electric efficiency of 38.9%, while tunable output flexibility of energy allocation between heat and power leads to both coal saving ratio and CO2 emission saving ratio in a wide range between 16.9% and 100%. Effective solar energy storage via methanol-derived syngas enables off-sun operations under normal energy demand conditions up to a few days, and attains round-the-clock heat supply with 41% carbon consumption and CO2 emission savings. The proposed system showcases a practical and efficient means of solar energy utilization complemented by fossil fuels, and provides a potential solution towards imminent energy and environmental challenges worldwide.