Reasoning by analogy is one of the most complex and highly adaptive cognitive processes in abstract thinking. For humans, analogical reasoning entails the judgment and conceptual mapping of relations-between-relations and is facilitated by language (Gentner in Cogn Sci 7:155-170, 1983; Premack in Thought without language, Oxford University Press, New York, 1986). Recent evidence, however, shows that monkeys like ``language-trained'' apes exhibit similar capacity to match relations-between-relations (Fagot and Thompson in Psychol Sci 22:1304-1309, 2011; Flemming et al. in J Exp Psychol: Anim Behav Process 37:353-360, 2011; Truppa et al. in Plos One 6(8):e23809, 2011). Whether this behavior is driven by the abstraction of categorical relations or alternatively by direct perception of variability (entropy) is crucial to the debate as to whether nonhuman animals are capable of analogical reasoning. In the current study, we presented baboons (Papio papio) and humans (Homo sapiens) with a computerized same/different relational-matching task that in principle could be solved by either strategy. Both baboons and humans produced markedly similar patterns of responding. Both species responded different when the perceptual variability of a stimulus array fell exactly between or even closer to that of a same display. Overall, these results demonstrate that categorical abstraction trumped perceptual properties and, like humans, Old World monkeys can solve the analogical matching task by judging the categorical abstract equivalence of same/different relations-between-relations.