Analysis of large data sets can help resolve difficult nodes in the tree of life and also concomitantly reveal complex evolutionary histories, including instances of lateral gene transfer, hybridization, or incomplete lineage sorting. The placement of the Celastrales-Oxalidales-Malpighiales (COM) clade within the large Rosidae clade remains one of the most difficult deep-level phylogenetic questions in angiosperms, with previous analyses placing it with either Fabidae (suggested by chloroplast genes) or Malvidae (suggested by mitochondrial and nuclear genes, as well as morphological data). To elucidate the underlying cause of this phylogenetic discordance, we assembled taxonomically comparable multi-gene matrices of chloroplast, mitochondrial, and nuclear sequences (82 taxa for 78 chloroplast genes, 79 taxa for 4 mitochondrial genes, and 92 taxa for 5 nuclear genes), as well as large single- and multi-copy nuclear gene data sets (8,445 single-copy ortholog sets and 3,748 multi-copy nuclear gene families). Analyses of multi-gene data sets demonstrate incongruence between the chloroplast and both nuclear and mitochondrial data sets, and the results are robust to various character-coding and data-exclusion treatments, not due to systematic biases or sampling errors. Analyses of single- and multi-copy nuclear genes indicate that most loci support the placement of COM with Malvidae, with a notable number of genes supporting COM with Fabidae, and almost no support for COM outside a clade of Malvidae and Fabidae. The proportion of genes supporting each hypothesis suggests that the phylogenetic incongruence is not due to incomplete lineage sorting, remaining ancient introgressive hybridization as a plausible explanation for the conflict among genes. In summary, our analyses demonstrate that the placement of COM clade with Malvidae better reflects organismal phylogeny, the conflicting phylogenetic placements for COM clade might be caused by ancient hybridization and chloroplast transmission occurred during the early and rapid radiation of Rosidae, and consequently resulted in conflict between chloroplast and mitochondrial gene trees, as well as a mixture of two underlying signals derived from its ancestral parents in the nuclear genome. Although greater taxon and nuclear genome sampling are necessary to evaluate such hypothesis fully, our study provides an example for examination of other deep nodes of the tree of life where conflict occurs among data sets from different subcellular compartments, and also emphasizes the importance of genomic data sets for revealing deep incongruence and potentially complex patterns of evolution in organismal phylogeny.