The Cretaceous–Palaeogene (K–Pg) mass extinction is linked to the rapid emergence of ecologically divergent higher taxa (for example, families and orders) across terrestrial vertebrates, but its impact on the diversification of marine vertebrates is less clear. Spiny-rayed fishes (Acanthomorpha) provide an ideal system for exploring the effects of the K–Pg on fish diversification, yet despite decades of morphological and molecular phylogenetic efforts, resolution of both early diverging lineages and enormously diverse subclades remains problematic. Recent multilocus studies have provided the first resolved phylogenetic backbone for acanthomorphs and suggested novel relationships among major lineages. However, these new relationships and associated timescales have not been interrogated using phylogenomic approaches. Here, we use targeted enrichment of >1,000 ultraconserved elements in conjunction with a divergence time analysis to resolve relationships among 120 major acanthomorph lineages and provide a new timescale for acanthomorph radiation. Our results include a well-supported topology that strongly resolves relationships along the acanthomorph backbone and the recovery of several new relationships within six major percomorph subclades. Divergence time analyses also reveal that crown ages for five of these subclades, and for the bulk of the species diversity in the sixth, coincide with the K–Pg boundary, with divergences between anatomically and ecologically distinctive suprafamilial clades concentrated in the first 10 million years of the Cenozoic.