As the supercontinent Pangaea fragmented during the Mesozoic era, dinosaur faunas were divided into isolated populations living on separate continents. It has been predicted, therefore, that dinosaur distributions should display a branching (‘vicariance’) pattern that corresponds with the sequence and timing of continental break‐up. Several recent studies, however, minimize the importance of plate tectonics and instead suggest that dispersal and regional extinction were the main controls on dinosaur biogeography. Here, in order to test the vicariance hypothesis, we apply a cladistic biogeographical method to a large dataset on dinosaur relationships and distributions. We also introduce a methodological refinement termed ‘time‐slicing’, which is shown to be a key step in the detection of ancient biogeographical patterns. These analyses reveal biogeographical patterns that closely correlate with palaeogeography. The results provide the first statistically robust evidence that, from Middle Jurassic to mid‐Cretaceous times, tectonic events had a major role in determining where and when particular dinosaur groups flourished. The fact that evolutionary trees for extinct organisms preserve such distribution patterns opens up a new and fruitful direction for palaeobiogeographical research.