Objective: As a critical component of lifeline infrastructure, urban power systems (UPSs) are essential for maintaining city functionality and supporting daily societal needs. Accurately assessing the post-earthquake functionality (PEF) of power systems is crucial due to its great importance for emergency response, urban recovery, and social stability. Traditional connectivity-based assessment methodstend to overestimate the post-earthquake power supply capability because they ignore the physical constraints of power transmission and distribution. To address this limitation, this study proposes a comprehensive PEF assessment framework to accurately quantify UPS performance under seismic scenarios. The framework explicitly integrates topology, physical damage, power redistribution, and cascading failures, providing reliable support for emergency decision-making and recovery planning. Methods: The proposed framework consists of five interrelated steps. (1) A unified topological representation of the UPS is derived using single-line diagrams, in which buses serve as core units and sources, while transformers, lines, and switching stations are consistently abstracted across voltage levels. (2) A spatially distributed ground-motion field over the urban area is generated, and engineering demand parameters (e.g., peak ground acceleration) are assigned to different electrical facilities. (3) Seismic damage scenarios, i.e., damage to substations, lines, and switching stations, are generated using Monte Carlo simulations. Each damage state is mapped to a reduction in power supply capacity, allowing partial functionality loss rather than a binary failure mode. Damaged components are removed from the network, while components with no power supply are identified and excluded through connectivity analysis. (4) DC power flow is executed within each source-connected island, with a slack bus to enforce power balance. Cascading failures are simulated by iteratively removing the lines that exceed their rated capacity until the system reaches a stable state. Load curtailment follows explicit rules: priority users are supplied first, and remaining capacity is proportionally distributed among non-priority users based on load weight. (5) The load-supply performance index (η_LS) is employed to quantify the overall and regional PEF of the UPS under seismic scenarios, incorporating land-use classifications and spatial zoning for differentiated analysis. Results: A case study was conducted on a benchmark city model representing a medium-sized coastal city in southeastern China with over 500 land parcels and a total forecasted load of 1 873.46 MW. The PEF of the UPS was assessed with 10 000 Monte Carlo realizations considering a seismic scenario in which an Mw 6.5 earthquake occurred 10 km northeast of the city center. The results showed that the average η_LS was 46.87%, with the most severe functionality losses concentrated in the northeastern region near the epicenter. Functionality varied across land-use types: logistic and public service lands showed the highest median functionality levels (>70.00%), while industrial lands exhibited high variability (median approximately 62.99%). Residential, green space, and commercial lands showed mean functionality levels of approximately 45.00%. The earthquake epicenter location strongly influenced UPS performance, with the η_LS degrading to 35.69%-37.88% when the earthquake occurred to the west, north, and northwest of the city. Conclusions: This study validates the applicability of the proposed DC power flow-based functionality assessment method. Key findings include: (1) the framework captures the influence of network topology, seismic input randomness, power redistribution, and cascading failures on the PEF of UPS; (2) cascading failures significantly amplify functionality loss because partially damaged components may become non-functional due to overloading or islanding effects; (3) functionality differs across land-use types, with logistic and public service lands performing best, industrial lands showing high variability, and residential, green, and commercial lands maintaining stability close to the system average; (4) earthquake epicenter orientation strongly affects system functionality, highlighting the need to locate high-demand areas away from potential seismic sources and improve redundancy in critical transmission paths; and (5) current limitations, including the absence of post-earthquake redispatch modeling and the simplified power flow representation, will be addressed in future studies.