Despite considerable interest in the forces shaping the relationship between brain size and cognitive abilities, it remains controversial whether larger-brained animals are, indeed, better problem-solvers. Recently, several comparative studies have revealed correlations between brain size and traits thought to require advanced cognitive abilities, such as innovation, behavioral flexibility, invasion success, and self-control. However, the general assumption that animals with larger brains have superior cognitive abilities has been heavily criticized, primarily because of the lack of experimental support for it. Here, we designed an experiment to inquire whether specific neuroanatomical or socioecological measures predict success at solving a novel technical problem among species in the mammalian order Carnivora. We presented puzzle boxes, baited with food and scaled to accommodate body size, to members of 39 carnivore species from nine families housed in multiple North American zoos. We found that species with larger brains relative to their body mass were more successful at opening the boxes. In a subset of species, we also used virtual brain endocasts to measure volumes of four gross brain regions and show that some of these regions improve model prediction of success at opening the boxes when included with total brain size and body mass. Socioecological variables, including measures of social complexity and manual dexterity, failed to predict success at opening the boxes. Our results, thus, fail to support the social brain hypothesis but provide important empirical support for the relationship between relative brain size and the ability to solve this novel technical problem.