The advent of Darwinian evolution required the emergence of molecular mechanisms for the heritable variation of fitness. One model for such a system involves competing protocell populations, each consisting of a replicating genetic polymer within a replicating vesicle. In this model, each genetic polymer imparts a selective advantage to its protocell by, for example, coding for a catalyst that generates a useful metabolite. Here, we report a partial model of such nascent evolutionary traits in a system that consists of fatty-acid vesicles containing a dipeptide catalyst, which catalyses the formation of a second dipeptide. The newly formed dipeptide binds to vesicle membranes, which imparts enhanced affinity for fatty acids and thus promotes vesicle growth. The catalysed dipeptide synthesis proceeds with higher efficiency in vesicles than in free solution, which further enhances fitness. Our observations suggest that, in a replicating protocell with an RNA genome, ribozyme-catalysed peptide synthesis might have been sufficient to initiate Darwinian evolution.