Did the end-Cretaceous mass extinction event, by eliminating non-avian dinosaurs and most of the existing fauna, trigger the evolutionary radiation of present-day mammals? Here we construct, date and analyse a species-level phylogeny of nearly all extant Mammalia to bring a new perspective to this question. Our analyses of how extant lineages accumulated through time show that net per-lineage diversification rates barely changed across the Cretaceous/Tertiary boundary. Instead, these rates spiked significantly with the origins of the currently recognized placental superorders and orders approximately 93 million years ago, before falling and remaining low until accelerating again throughout the Eocene and Oligocene epochs. Our results show that the phylogenetic `fuses' leading to the explosion of extant placental orders are not only very much longer than suspected previously, but also challenge the hypothesis that the end-Cretaceous mass extinction event had a major, direct influence on the diversification of today's mammals.