In order to enhance the carbon reduction potential of a park, a low-carbon economic dispatch method applicable to zero-carbon parks is proposed to optimize the energy dispatch of the park at multiple timescales; this is achieved by introducing a flexible response mechanism for source–load bilaterals, so as to achieve low-carbon, economic, and efficient operation. First, a park model that accounts for the energy flow characteristics and carbon potential distribution of the energy hub is established. Then, based on the flexible operation of energy supply equipment and multi-type integrated demand response, the flexible response mechanism of source–load bilaterally and the multi-timescale scheduling framework are proposed; the mechanisms of source–load coordination and electricity–carbon coupling are analyzed in depth. Finally, with the objective of optimal system operation economy, the optimal scheduling model is established for three timescales, namely, day-ahead, intraday, and real-time scheduling. The equipment output and demand response are optimized step by step according to the source–load prediction information and scheduling results at each stage. The simulation results show that the proposed model can effectively utilize the source and load resources to participate in scheduling and can effectively reduce carbon emissions while ensuring the energy supply demand of the park, realizing the low-carbon, economic operation of the system. Therefore, this study provides a new theoretical basis and practical solution for the optimal dispatch of energy in zero-carbon parks, which helps to promote the development of a low-carbon economy.