Addressing phylogenetic problems using complex genomic datasets usually proceeds either via concatenation of all gene sequences into a supermatrix for model-based analysis or by estimation of individual gene genealogies to produce a summary tree under the coalescent. No approach is without shortcomings, as concatenation can amplify undesired biases and coalescent approaches can be sensitive to gene tree estimation error. Here, we present a method to account for gene tree error in genome-wide datasets by individually interrogating gene fragments in a statistical framework using topology tests. We apply this method to resolve controversial relationships within the largest freshwater fish radiation using newly generated exon-wide data (1051 loci) for 225 species. While both concatenation and coalescent methods reveal substantial incongruence, our novel approach resolves the interrelationships of major lineages with high confidence. We investigate the utility of our method by reanalysing published datasets for other emblematic groups proven recalcitrant to phylogenetic resolution.