The origins and the divergence times of the most basal lineages within primates have been difficult to resolve mainly due to the incomplete sampling of early fossil taxa. The main source of contention is related to the discordance between molecular and fossil estimates: while there are no crown primate fossils older than 56 Ma, most molecule-based estimates extend the origins of crown primates into the Cretaceous. Here we present a comprehensive mitogenomic study of primates. We assembled 87 mammalian mitochondrial genomes, including 62 primate species representing all the families of the order. We newly sequenced eleven mitochondrial genomes, including eight Old World monkeys and three strepsirrhines. Phylogenetic analyses support a strong topology, confirming the monophyly for all the major primate clades. In contrast to previous mitogenomic studies, the positions of tarsiers and colugos relative to strepsirrhines and anthropoids are well resolved. In order to improve our understanding of how fossil calibrations affect age estimates within primates, we explore the effect of seventeen fossil calibrations across primates and other mammalian groups and we select a subset of calibrations to date our mitogenomic tree. The divergence date estimates of the Strepsirrhine/Haplorhine split support an origin of crown primates in the Late Cretaceous, at around 74 Ma. This result supports a short-fuse model of primate origins, whereby relatively little time passed between the origin of the order and the diversification of its major clades. It also suggests that the early primate fossil record is likely poorly sampled.