The fossil record suggests a rapid radiation of placental mammals following the Cretaceous-Paleogene (K-Pg) mass extinction 65 million years ago (Ma); nevertheless, molecular time estimates, while highly variable, are generally much older. Early molecular studies suffer from inadequate dating methods, reliance on the molecular clock, and simplistic and over-confident interpretations of the fossil record. More recent studies have used Bayesian dating methods that circumvent those issues, but the use of limited data has led to large estimation uncertainties, precluding a decisive conclusion on the timing of mammalian diversifications. Here we use a powerful Bayesian method to analyse 36 nuclear genomes and 274 mitochondrial genomes (20.6 million base pairs), combined with robust but flexible fossil calibrations. Our posterior time estimates suggest that marsupials diverged from eutherians 168-178 Ma, and crown Marsupialia diverged 64-84 Ma. Placentalia diverged 88-90 Ma, and present-day placental orders (except Primates and Xenarthra) originated in a ∼20 Myr window (45-65 Ma) after the K-Pg extinction. Therefore we reject a pre K-Pg model of placental ordinal diversification. We suggest other infamous instances of mismatch between molecular and palaeontological divergence time estimates will be resolved with this same approach.