The development of emerging technologies has enhanced the demand response (DR) capability of conventional loads. To study the effect of DR on the reduction in carbon emissions in an integrated energy system (IES), a two-stage low-carbon economic dispatch model based on the carbon emission flow (CEF) theory was proposed in this study. In the first stage, the energy supply cost was taken as the objective function for economic dispatch, and the actual carbon emissions of each energy hub (EH) were calculated based on the CEF theory. In the second stage, a low-carbon DR optimization was performed with the objective function of the load-side carbon trading cost. Then, based on the modified IEEE 39-bus power system/Belgian 20-node natural gas system, MATLAB/Gurobi was used for the simulation analysis in three scenarios. The results showed that the proposed model could effectively promote the system to reduce the load peak-to-valley difference, enhance the ability to consume wind power, and reduce the carbon emissions and carbon trading cost. Furthermore, as the wind power penetration rate increased from 20% to 80%, the carbon reduction effect basically remained stable. Therefore, with the growth of renewable energy, the proposed model can still effectively reduce carbon emissions.