The origin of digit-bearing tetrapods in the Middle to Late Devonian (ca. 393-360 Mya) and their subsequent invasion of land represent a classic case of a major evolutionary radiation driven by new ecological opportunities. In this and other examples, exploration of new eco-space is hypothesized to correlate with functional innovation and adaptive divergence of phenotypes. Simultaneous changes in all morphofunctional systems are rare in major evolutionary transitions and may be non-existent. Here, we focus on the mandibles of early tetrapods and their kin as a model system to test whether shifts in functional innovation were coeval with some major events in tetrapod history. To this end, we quantified mechanical variation in the mandibles of tetrapodomorphs ranging in age from Early Devonian to earliest Permian. Biomechanical disparity is stable from the Devonian to the Early Pennsylvanian, even though the origin of weight-bearing, digited limbs, and the initial phases of the colonization of land occurred during this interval. An appreciable increase in functional variation is detected in the latest Pennsylvanian and earliest Permian, when stem and crown amniotes began to explore new regions of mechanical morphospace, a pattern partly attributable to the origin of herbivory. We find no difference in the rate of functional change between tetrapodomorph "fish" and early digited tetrapods, although two independent shifts are detected among Devonian stem tetrapods more crownward than Acanthostega. Instead, the most profound shifts in evolutionary rate are nested well within the tetrapod crown and are associated with amniotes (particularly diadectomorphs and some synapsids). The substantial temporal gap between the origin of postcranial features associated with terrestriality, such as limbs with functional elbow/knee and wrist/ankle joints capable of weight-bearing, and the onset of divergence in jaw biomechanics provides a compelling example of "functional modularity" during a major adaptive radiation.