Understanding the relationship between vegetation structure and functional stability is essential for assessing and maintaining urban ecosystems as global urban expansion continues. This study combines global 1-meter resolution canopy height data with long-term EVI to analyze spatial patterns and structural-functional relationships of vegetation across urban-rural gradients in 53 major cities worldwide. Our results show a nonlinear threshold response of vegetation functional stability (CV) to both canopy height and EVI. Temporal variability was minimized within an optimal stability zone, specifically at canopy heights of 14-16 m and EVI values around 0.53-0.55. When vegetation structure or function deviated from this zone, stability declined, forming a U-shaped relationship. These thresholds varied with climatic and urban contexts, generally higher in arid regions and urban cores, and lower in warm temperate zones and suburban areas. Globally, vegetation in most cities remained below optimal thresholds, with suburban areas closer to the stability threshold. Additionally, multiple patterns of structural-functional decoupling were observed along the gradient. In some cities, high functional stability was maintained even under low structural development, likely due to intensive management. In others, functional stability improved without significant structural changes, possibly buffered by surrounding seminatural vegetation. In areas where both structure and function were low, temporal variability reflected a state of reduced function and limited resilience. This study provides a framework for identifying stability mechanisms and offers insights for targeted green-space planning, emphasizing the importance of maintaining vegetation within its optimal stability range for climate adaptation and ecological resilience.