Effectively utilizing the low-carbon potential of demand-side resources to coordinate with medium- and low-voltage distribution network scheduling, thereby reducing system carbon emissions, is crucial for China’s “dual carbon” strategy. To address this issue, a new low-carbon scheduling method for distribution networks is proposed, considering dynamic carbon potential and demand response. First, the influence of the superior grid’s dynamic carbon potential and distribution network losses on carbon emission flow is analyzed, and accounting models for user-side electricity consumption emissions and network loss emissions are established. Second, an incentive-based demand response model based on dynamic carbon potential is developed. By adjusting low-carbon incentive prices according to time-varying carbon potential, users are guided to regulate flexible loads to reduce electricity-related carbon emissions. Then, a low-carbon scheduling model for distribution networks is created. It balances operational safety and economy, while the distribution network’s dynamic carbon potential guides the demand response to achieve low-carbon and safe system operation at minimal activation cost. Finally, case studies on a modified IEEE 33-node system demonstrate the effectiveness of the proposed model and method, reducing network losses by 7.3%, daily peak-valley load difference by 11.7%, and carbon emissions by 3.5%.