The evolution of primates involved increasing body size, brain size and presumably cognitive ability. Cognition is related to neural activity, metabolic rate and rate of blood flow to the cerebral cortex. These parameters are difficult to quantify in living animals. This study shows that it is possible to determine the rate of cortical brain perfusion from the size of the internal carotid artery foramina in skulls of certain mammals, including haplorrhine primates and diprotodont marsupials. We quantify combined blood flow rate in both internal carotid arteries as a proxy of brain metabolism in 34 species of haplorrhine primates (0.116-145 kg body mass) and compare it to the same analysis for 19 species of diprotodont marsupials (0.014-46 kg). Brain volume is related to body mass by essentially the same exponent of 0.70 in both groups. Flow rate increases with haplorrhine brain volume to the 0.95 power, which is significantly higher than the exponent (0.75) expected for most organs according to 'Kleiber's Law'. By comparison, the exponent is 0.73 in marsupials. Thus, the brain perfusion rate increases with body size and brain size much faster in primates than in marsupials. The trajectory of cerebral perfusion in primates is set by the phylogenetically older groups (New and Old World monkeys, lesser apes) and the phylogenetically younger groups (great apes, including humans) fall near the line, with the highest perfusion. This may be associated with disproportionate increases in cortical surface area and mental capacity in the highly social, larger primates.