Alternative models of evolutionary processes suggest different associations between species diversification and trait evolution, but limited empirical evidence is available to test these models across large clades at global extents. Here we investigate the relative timing of species diversification and niche and phenotypic evolution across a global plant radiation (Saxifragales) with enormous phenotypic and habitat variation. We demonstrate strong temporal lags among rates, with increased diversification occurring first, followed by niche and phenotype. Accelerated diversification rates are coincident with mid-Miocene expansion of temperate biomes. Later increases in niche and phenotypic evolutionary rates argue against density-dependent diversification alone, indicating a major role for ecological opportunity. These results have broad implications for understanding diversification processes and the origin of present-day temperate biotas.