Placental mammals comprise three principal clades: Afrotheria (e.g. elephants and tenrecs), Xenarthra (e.g. armadillos and sloths) and Boreoeutheria (all other placental mammals), the relationships among which are the subject of controversy and a touchstone for debate on the limits of phylogenetic inference. Previous analyses have found support for all three hypotheses, leading some to conclude that this phylogenetic problem might be impossible to resolve, due to the compounded effects of Incomplete Lineage Sorting (ILS) and a rapid radiation. Here we show, using a genome scale nucleotide dataset, microRNAs, and the reanalysis of the three largest previously published amino-acid datasets, that the root of Placentalia lies between Atlantogenata and Boreoeutheria. Although we found evidence for ILS in early placental evolution, we are able to reject previous conclusions that the placental root is a hard polytomy that cannot be resolved. Reanalyses of previous datasets recover Atlantogenata + Boreoeutheria and show that contradictory results are a consequence of poorly fitting evolutionary models; instead, when the evolutionary process is better-modelled, all datasets converge on Atlantogenata. Our Bayesian molecular clock analysis estimates that marsupials diverged from placentals 157-170 Ma, crown Placentalia diverged 86-100 Ma, and crown Atlantogenata diverged 84-97 Ma. Our results are compatible with placental diversification being driven by dispersal rather than vicariance mechanisms, postdating early phases in the protracted opening of the Atlantic Ocean.