Conodonts are an extinct group of jawless vertebrates whose tooth-like elements are the earliest instance of a mineralized skeleton in the vertebrate lineage, inspiring the ‘inside-out’ hypothesis that teeth evolved independently of the vertebrate dermal skeleton and before the origin of jaws. However, these propositions have been based on evidence from derived euconodonts. Here we test hypotheses of a paraconodont ancestry of euconodonts using synchrotron radiation X-ray tomographic microscopy to characterize and compare the microstructure of morphologically similar euconodont and paraconodont elements. Paraconodonts exhibit a range of grades of structural differentiation, including tissues and a pattern of growth common to euconodont basal bodies. The different grades of structural differentiation exhibited by paraconodonts demonstrate the stepwise acquisition of euconodont characters, resolving debate over the relationship between these two groups. By implication, the putative homology of euconodont crown tissue and vertebrate enamel must be rejected as these tissues have evolved independently and convergently. Thus, the precise ontogenetic, structural and topological similarities between conodont elements and vertebrate odontodes appear to be a remarkable instance of convergence. The last common ancestor of conodonts and jawed vertebrates probably lacked mineralized skeletal tissues. The hypothesis that teeth evolved before jaws and the inside-out hypothesis of dental evolution must be rejected; teeth seem to have evolved through the extension of odontogenic competence from the external dermis to internal epithelium soon after the origin of jaws.