A fundamental challenge in resolving evolutionary relationships across the tree of life is to account for heterogeneity in the evolutionary signal across loci. Studies of marsupial mammals have demonstrated that this heterogeneity can be substantial, leaving considerable uncertainty in the evolutionary timescale and relationships within the group. Using simulations and a new phylogenomic data set comprising nucleotide sequences of 1550 loci from 18 of the 22 extant marsupial families, we demonstrate the power of a method for identifying clusters of loci that support different phylogenetic trees. We find two distinct clusters of loci, each providing an estimate of the species tree that matches previously proposed resolutions of the marsupial phylogeny. We also identify a well-supported placement for the enigmatic marsupial moles (Notoryctes) that contradicts previous molecular estimates but is consistent with morphological evidence. The pattern of gene-tree variation across tree-space is characterized by changes in information content, GC content, substitution-model adequacy, and signatures of purifying selection in the data. In a simulation study, we show that incomplete lineage sorting can explain the division of loci into the two tree-topology clusters, as found in our phylogenomic analysis of marsupials. We also demonstrate the potential benefits of minimizing uncertainty from phylogenetic conflict for molecular dating. Our analyses reveal that Australasian marsupials appeared in the early Paleocene, whereas the diversification of present-day families occurred primarily during the late Eocene and early Oligocene. Our methods provide an intuitive framework for improving the accuracy and precision of phylogenetic inference and molecular dating using genome-scale data.