Divergence times estimated from molecular data often considerably predate the earliest known fossil representatives of the groups studied. For the order Primates, molecular data calibrated with various external fossil dates uniformly suggest a mid-Cretaceous divergence from other placental mammals, some 90 million years (Myr) ago, whereas the oldest known fossil primates are from the basal Eocene epoch (54-55 Myr ago). The common ancestor of primates should be earlier than the oldest known fossils, but adequate quantification is needed to interpret possible discrepancies between molecular and palaeontological estimates. Here we present a new statistical method, based on an estimate of species preservation derived from a model of the diversification pattern, that suggests a Cretaceous last common ancestor of primates, approximately 81.5 Myr ago, close to the initial divergence time inferred from molecular data. It also suggests that no more than 7% of all primate species that have ever existed are known from fossils. The approach unites all the available palaeontological methods of timing evolutionary events: the fossil record, extant species and clade diversification models.