Residential energy management (REM) is an important way to encourage users to reduce or shift energy demand with dynamic pricing. It could significantly affect the supply–demand relationship between electricity service providers (ESPs) and users, reduce energy cost and consumption, and contribute to sustainable development. To improve latency and processing performance, a three-tier edge-cloud collaborative REM (ECCREM) architecture is presented. In consideration of matching the architecture, a two-stage energy management mechanism is proposed with system reliability and resource utilization requirements taken into account. At the first stage, the interaction between real-time pricing and energy demand is modeled by a Stackelberg and Lyapunov-based pricing and energy demand joint optimization (SLPEDO) algorithm. At the second stage, two procedures, i.e., energy scheduling between a cloud tier and an access tier, and energy scheduling between an access tier and an infrastructure tier, are implemented. A priority-based demand ratio sequentially scheduling strategy is proposed to address energy scheduling in these two procedures, respectively. Simulation results show that compared with the existing demand ratio-based scheduling and equally scheduling strategies, the proposed strategy can improve overall satisfaction of users by up to 20%. In addition, energy cost can be reduced and demand fluctuation relieved.