Tyrannosaurus rex and other tyrannosaurid dinosaurs were apex predators during the latest Cretaceous, which combined giant size and advanced neurosensory systems. Computed tomography (CT) data have shown that tyrannosaurids had a trademark system of a large brain, large olfactory bulbs, elongate cochlear ducts, and expansive endocranial sinuses surrounding the brain and sense organs. Older, smaller tyrannosauroid relatives of tyrannosaurids developed some, but not all, of these features, raising the hypothesis that tyrannosaurid‐style brains evolved before the enlarged tyrannosaurid‐style sinuses, which might have developed only with large body size. This has been difficult to test, however, because little is known about the brains and sinuses of the first large‐bodied tyrannosauroids, which evolved prior to Tyrannosauridae. We here present the first CT data for one of these species, Bistahieversor sealeyi from New Mexico. Bistahieversor had a nearly identical brain and sinus system as tyrannosaurids like Tyrannosaurus, including a large brain, large olfactory bulbs, reduced cerebral hemispheres, and optic lobes, a small tab‐like flocculus, long and straight cochlear ducts, and voluminous sinuses that include a supraocciptal recess, subcondyar sinus, and an anterior tympanic recess that exits the braincase via a prootic fossa. When characters are plotted onto tyrannosauroid phylogeny, there is a two‐stage sequence in which features of the tyrannosaurid‐style brain evolved first (in smaller, nontyrannosaurid species like Timurlengia), followed by features of the tyrannosaurid‐style sinuses (in the first large‐bodied nontyrannosaurid tyrannosauroids like Bistahieversor). This suggests that the signature tyrannosaurid sinus system evolved in concert with large size, whereas the brain did not. Anat Rec, 303:1043–1059, 2020. © 2020 American Association for Anatomy