How biodiversity is generated and maintained underlies many major questions in evolutionary biology, particularly relating to the tempo and pattern of diversification through time. Molecular phylogenies and new analytical methods provide additional tools to help interpret evolutionary processes. Evolutionary rates in lineages sometimes appear punctuated, and such “explosive” radiations are commonly interpreted as adaptive, leading to causative key innovations being sought. Here we argue that an alternative process might explain apparently rapid radiations (“broom-and-handle” or “stemmy” patterns seen in many phylogenies) with no need to invoke dramatic increase in the rate of diversification. We use simulations to show that mass extinction events can produce the same phylogenetic pattern as that currently being interpreted as due to an adaptive radiation. By comparing simulated and empirical phylogenies of Australian and southern African legumes, we find evidence for coincident mass extinctions in multiple lineages that could have resulted from global climate change at the end of the Eocene.