The electric power system is the most critical component of urban infrastructure, serving as the foundation for the normal operation of a city. Earthquakes have a substantial impact on urban power systems. On one hand, it is reflected in the extensive damage to power infrastructure and the widespread power outages. On the other hand, it manifests in the long recovery times for power facilities and the significant impact on people’s livelihoods. Therefore, the performance analysis of the power system under seismic conditions and the post-earthquake restoration process urgently require attention. To more accurately assess and enhance the seismic resilience of urban power systems, a quantitative analysis framework for seismic resilience from a functional perspective has been established. The performance index of the power system is defined as the ratio of the population receiving power to the total population after an earthquake. The initial damage is determined through the seismic vulnerability modeling of power system components. The cascading failures of the power system following an earthquake are simulated using the DC power flow method to assess the power surplus in the city post-earthquake. The damaged components are then repaired, and the seismic resilience index is obtained by solving the system’s performance-time curve through an integral method. Based on functional analysis methods and component importance theory, the concept of post-earthquake restoration step length for the power system has been proposed. By adjusting the restoration step length, three restoration strategies have been developed including dynamic importance-based, static importance-based, and hybrid importance-based restoration strategies. A case study of a power grid in China has been conducted to validate the effectiveness of the resilience assessment framework and restoration strategies. The results show that the functional-based power system resilience assessment framework can effectively perform post-earthquake performance analysis and generate functional curves. The DC power flow analysis method accurately determines the state of each line and node in the power system, enabling a more realistic and reasonable simulation of cascading failures in the power system after an earthquake. Under 10,000 Monte Carlo simulations, the frequency distribution, average value, and the maximum value of the restoration strategy based on dynamic importance theory are significantly higher than those of the static importance-based strategy. The dynamic importance strategy yields the highest seismic resilience index, while the hybrid importance strategy provides intermediate results, and the static importance strategy results in the lowest seismic resilience index. The computational time required is inversely related to the resilience index, with the dynamic importance strategy taking 25 times longer than the static importance strategy. The hybrid importance strategy, which balances dynamic and static factors, has been shown to be the most efficient recovery strategy when dealing with large-scale computations and multiple scenarios, as it ensures higher resilience while maintaining computational efficiency.