The origin of jaws remains largely an enigma that is best addressed by studying fossil and living jawless vertebrates. Conodonts were eel-shaped jawless animals, whose vertebrate affinity is still disputed. The geometrical analysis of exceptional three-dimensionally preserved clusters of oro-pharyngeal elements of the Early Triassic Novispathodus, imaged using propagation phase-contrast X-ray synchrotron microtomography, suggests the presence of a pulley-shaped lingual cartilage similar to that of extant cyclostomes within the feeding apparatus of euconodonts ("true" conodonts). This would lend strong support to their interpretation as vertebrates and demonstrates that the presence of such cartilage is a plesiomorphic condition of crown vertebrates.