Lactate and malate dehydrogenases (LDH and MDH) are homologous, core metabolic enzymes common to nearly all living organisms. LDHs have evolved convergently from MDHs at least four times, achieving altered substrate specificity by a different mechanism each time. For instance, the LDH of anaerobic trichomonad parasites recently evolved independently from an ancestral trichomonad MDH by gene duplication. LDH plays a central role in trichomonad metabolism by catalyzing the reduction of pyruvate to lactate, thereby regenerating the NAD1 required for glycolysis. Using ancestral reconstruction methods, we identified the biochemical and evolutionary mechanisms responsible for this convergent event. The last common ancestor of these enzymes was a highly specific MDH, similar to modern trichomonad MDHs. In contrast, the LDH lineage evolved promiscuous activity by relaxing specificity in a gradual process of neofunctionalization involving one highly detrimental substitution at the "specificity residue" (R91L) and many additional mutations of small effect. L91 has different functional consequences in LDHs and in MDHs, indicating a prominent role for epistasis. Crystal structures of modern-day and ancestral enzymes show that the evolution of substrate specificity paralleled structural changes in dimerization and a-helix orientation. The relatively small "specificity residue" of the trichomonad LDHs can accommodate a range of substrate sizes and may permit solvent to access the active site, both of which promote substrate promiscuity. The trichomonad LDHs present a multi-faceted counterpoint to the independent evolution of LDHs in other organisms and illustrate the diverse mechanisms by which protein function, structure, and stability coevolve.