Understanding impacts on species diversification is fundamental to our understanding of the evolutionary processes underlying biodiversity. The 'behavioural drive hypothesis' posits that behavioural innovation, coupled with the social transmission of innovative behaviours, can increase rates of evolution and diversification, as novel behaviours expose individuals to new selection regimes. We test this hypothesis within the primates, a taxonomic group with considerable among-lineage variation in both species diversity and behavioural flexibility. We employ a time cut-off in our phylogeny to help account for biases associated with recent taxonomic reclassifications and compare three alternative measures of diversification rate that consider different phylogenetic depths. We find that the presence of behavioural innovation and social learning are positively correlated with diversification rates among primate genera, but not at shallower taxonomic depths. Given that we find stronger associations when examining older as opposed to newer diversification events even after controlling for potential sampling biases, we suggest that extinction resistance may be an important mechanism linking behavioural flexibility and diversification in primates. If true, our findings offer support for an expanded view of the behavioural drive hypothesis, and key predictions of this hypothesis can be tested as primates are forced to respond to ongoing environmental change.