The dynamic charging behavior of electric vehicles (EVs) is causing frequent line-overloading problems and serious power security issues. Controlled and smart charging mechanisms for EVs incorporating demand response (DR) may provide significant operational flexibility to the grid operators and reduce charging costs for EV users. However, controlling EV charging may cause inconvenience to individual EV users. A market-based mechanism is proposed in this research work that allows EV users and households to participate in the network congestion alleviation DR program online while maintaining the power quality. Consumers submit their charging requirements (e.g., charging power and charging deadlines) and load curtailment tolerances to the aggregator. The aggregator is an entity assumed to have a long-term contract with the distribution system operator (DSO) and regularly receives network congestion information on behalf of retail energy users. Lyapunov optimization (LO) framework is used to reschedule the EVs, and household loads using DC optimal power flow (DCOPF) to get the dynamic congestion cost signal (CCS). The developed strategy is tested on a modified IEEE 33-bus radial active distribution network (ADN). Simulation results illustrate that the designed algorithm is promising in mitigating network congestion by ensuring significantly fewer violations of network constraints (i.e., line limits) both in terms of capacity and frequency. It also results in less energy cost as compared to other benchmark algorithms, e.g., greedy algorithm, and provides a guarantee of meeting EV charging, and flexible household loads’ (FHL) delay tolerance constraints. The average curtailment ratio of FHL and the service delay for EV-charging requests are converged to the user-defined limits, i.e., 0.25 for curtailment ratio tolerance and 10 times-lots for EV service delay. Unlike other counterparts, the developed algorithm is especially suitable for real-time applications as the per-slot average computational cost is negligible, i.e., 0.55 s.