This study proposes an innovative integrated method for evaluating the evacuation and rescue capabilities of open spaces through a case study in Wuhan, China. A dual-scenario network analysis model was set up to calculate travel time among communities, open spaces, and rescue facilities during peak and non-peak hours. The distribution of traffic flow was derived on the basis of a gravity model and used to construct supply-demand indexes (SDIs). SDIs such as evacuation (ESDI), rescue (RSDI), and comprehensive SDIs (CSDI) were used to evaluate the suitability of open space locations. This study drew five major findings as follows: (1) ESDI, RSDI, and CSDI can effectively evaluate the spatial suitability of open spaces when these SDIs are integrated with the gravity model. (2) The quadrant distribution analysis of ESDI can be an effective method for determining the reasons for the change in values in the two traffic scenarios and for helping planners in adjusting their policies to enhance the capability of an area. (3) The impact of the different β values on SDIs can show positive, negative, and inconspicuous correlations with large, moderate, and minimal variations, respectively. (4) The analysis of the supply-demand relationship of open spaces in Wuhan indicates a spatial mismatch in comprehensive evacuation and rescue capacities. (5) Traffic congestion can be a significant impact factor on evacuation and rescue capabilities but not on comprehensive capability.