Variation in the geographic spread of fossil localities strongly biases inferences about the evolution of biodiversity, due to the ubiquitous scaling of species richness with area. This obscures answers to key questions, such as how tetrapods attained their tremendous extant diversity. Here, we address this problem by applying sampling-standardisation methods to spatial regions of equal size, within a global Mesozoic–early Palaeogene dataset of non-flying terrestrial tetrapods. We recover no significant increase in species richness between the Late Triassic and the Cretaceous/Palaeogene (K/Pg) boundary, strongly supporting bounded diversification in Mesozoic tetrapods. An abrupt tripling of richness in the earliest Palaeogene suggests that this diversity equilibrium was reset following the K/Pg extinction. Spatial heterogeneity in sampling is among the most important biases of fossil data, but has often been overlooked. Our results indicate that controlling for variance in geographic spread in the fossil record significantly impacts inferred patterns of diversity through time.