Humans retain high covariation between cortical areas into adulthood unlike great apes. Great apes show high brain covariation only in juveniles. Hominins experienced higher evolutionary rates of brain covariation than all other primates. Strong brain covariation in humans and Neanderthals evolved faster than in any primate. Natural selection favored greatly integrated brains in humans and Neanderthals. Results hold excluding extinct species and after accounting for allometry. High brain covariation enabled unique cognitive capacities and complex behaviors in both species. Modern humans show distinct developmental patterns of brain covariation. Analysis used 400 endocasts from 148 primate species and 6 fossil hominins.