Worm lizards (Amphisbaenia) are burrowing squamates that live as subterranean predators. Their underground existence should limit dispersal, yet they are widespread throughout the Americas, Europe and Africa. This pattern was traditionally explained by continental drift, but molecular clocks suggest a Cenozoic diversification, long after the break-up of Pangaea, implying dispersal. Here, we describe primitive amphisbaenians from the North American Palaeocene, including the oldest known amphisbaenian, and provide new and older molecular divergence estimates for the clade, showing that worm lizards originated in North America, then radiated and dispersed in the Palaeogene following the Cretaceous-Palaeogene (K-Pg) extinction. This scenario implies at least three trans-oceanic dispersals: from North America to Europe, from North America to Africa and from Africa to South America. Amphisbaenians provide a striking case study in biogeography, suggesting that the role of continental drift in biogeography may be overstated. Instead, these patterns support Darwin and Wallace's hypothesis that the geographical ranges of modern clades result from dispersal, including oceanic rafting. Mass extinctions may facilitate dispersal events by eliminating competitors and predators that would otherwise hinder establishment of dispersing populations, removing biotic barriers to dispersal.