The spiny-finned teleost fishes (Acanthomorpha) include nearly one-third of all living vertebrate species and assume a bewildering array of bodyplans, but the macroevolutionary assembly of modern acanthomorph biodiversity remains largely unexplored. Here, I reconstruct the trajectory of morphological diversification in this major radiation from its first appearance in the Late Cretaceous to the Miocene using a geometric morphometric database comprising more than 600 extinct species known from complete body fossils. The anatomical diversity (disparity) of acanthomorphs is low throughout the Cretaceous, increases sharply and significantly in the wake of the Cretaceous-Palaeogene (K-P) extinction, and shows little change throughout subsequent Cenozoic intervals. This pattern of morphological diversification appears robust to two potential biasing factors: the 'Lagerstätten effect', and the non-random segregation of rare and common taxa along phenotypic axes. Dissecting the trajectory of acanthomorph radiation along phylogenetic lines reveals that the abrupt post-extinction increase in disparity is driven largely by the proliferation of trophically diverse modern groups within Percomorpha, a spiny-fin subclade containing more than 15 000 living species and identified as showing a substantially elevated diversification rate relative to background vertebrate levels. A major component of the Palaeogene acanthomorph radiation reflects colonization of morphospace previously occupied by non-acanthomorph victims of the K-P. However, other aspects of morphological diversification cannot be explained by this simple ecological release model, suggesting that multiple factors contributed to the prolific anatomical radiation of acanthomorphs.