Despite large-scale molecular attempts, the relationships of the basal winged insect lineages dragonflies, mayflies and neopterans, are still unresolved. Other data sources, such as morphology, suffer from unclear functional dependencies of the structures considered, which might mislead phylogenetic inference. Here, we assess this problem by combining for the first time biomechanics with phylogenetics using two advanced engineering techniques, multibody dynamics analysis and finite-element analysis, to objectively identify functional linkages in insect head structures which have been used traditionally to argue basal winged insect relationships. With a biomechanical model of unprecedented detail, we are able to investigate the mechanics of morphological characters under biologically realistic load, i.e. biting. We show that a range of head characters, mainly ridges, endoskeletal elements and joints, are indeed mechanically linked to each other. An analysis of character state correlation in a morphological data matrix focused on head characters shows highly significant correlation of these mechanically linked structures. Phylogenetic tree reconstruction under different data exclusion schemes based on the correlation analysis unambiguously supports a sistergroup relationship of dragonflies and mayflies. The combination of biomechanics and phylogenetics as it is proposed here could be a promising approach to assess functional dependencies in many organisms to increase our understanding of phenotypic evolution.