Large brains, relative to body size, can confer advantages to individuals in the form of behavioral flexibility. Such enhanced behavioral flexibility is predicted to carry fitness benefits to individuals facing novel or altered environmental conditions, a theory known as the brain size-environmental change hypothesis. Here, we provide the first empirical link between brain size and survival in novel environments in mammals, the largest-brained animals on Earth. Using a global database documenting the outcome of more than 400 introduction events, we show that mammal species with larger brains, relative to their body mass, tend to be more successful than species with smaller brains at establishing themselves when introduced to novel environments, when both taxonomic and regional autocorrelations are accounted for. This finding is robust to the effect of other factors known to influence establishment success, including introduction effort and habitat generalism. Our results replicate similar findings in birds, increasing the generality of evidence for the idea that enlarged brains can provide a survival advantage in novel environments.