Large-scale adaptive radiations might explain the runaway success of a minority of extant vertebrate clades. This hypothesis predicts, among other things, rapid rates of morphological evolution during the early history of major groups, as lineages invade disparate ecological niches. However, few studies of adaptive radiation have included deep time data, so the links between extant diversity and major extinct radiations are unclear. The intensively studied Mesozoic dinosaur record provides a model system for such investigation, representing an ecologically diverse group that dominated terrestrial ecosystems for 170 million years. Furthermore, with 10,000 species, extant dinosaurs (birds) are the most speciose living tetrapod clade. We assembled composite trees of 614-622 Mesozoic dinosaurs/birds, and a comprehensive body mass dataset using the scaling relationship of limb bone robustness. Maximum-likelihood modelling and the node height test reveal rapid evolutionary rates and a predominance of rapid shifts among size classes in early (Triassic) dinosaurs. This indicates an early burst niche-filling pattern and contrasts with previous studies that favoured gradualistic rates. Subsequently, rates declined in most lineages, which rarely exploited new ecological niches. However, feathered maniraptoran dinosaurs (including Mesozoic birds) sustained rapid evolution from at least the Middle Jurassic, suggesting that these taxa evaded the effects of niche saturation. This indicates that a long evolutionary history of continuing ecological innovation paved the way for a second great radiation of dinosaurs, in birds. We therefore demonstrate links between the predominantly extinct deep time adaptive radiation of non-avian dinosaurs and the phenomenal diversification of birds, via continuing rapid rates of evolution along the phylogenetic stem lineage. This raises the possibility that the uneven distribution of biodiversity results not just from large-scale extrapolation of the process of adaptive radiation in a few extant clades, but also from the maintenance of evolvability on vast time scales across the history of life, in key lineages.