Existing research on crude oil trade networks has largely focused on their static structural characteristics. However, systematic quantitative assessments of network stability, as well as examinations of the relationship between structural characteristics and stability, remain relatively limited. Based on United Nations Commodity Trade Statistics from 2000 to 2023, this study constructs an international crude oil trade network. By integrating complex network analysis with spatiotemporal methods, the study examines the network’s evolutionary patterns, evaluates its stability from both topological and flow dimensions using Jaccard similarity and weighted similarity indicators, and applies Spearman’s rank correlation to explore the associations between structural characteristics and stability. The results indicate that the following: (1) the international crude oil trade network exhibits a hierarchical core-periphery structure, with overall trade linkages between countries becoming increasingly tight; (2) key inflection points in network stability are correlated with major international events, and these correlations manifest differently across the dimensions of trade structure and trade flows; and (3) modularity is negatively correlated with topological stability and positively correlated with flow stability, while degree assortativity shows no significant association with either topological stability or flow stability, revealing that although the core-periphery structure enhances the resilience of trade scale, it may simultaneously weaken the flexibility of partnerships.