Michael Dixon's trip from goat to hero took all of 25 seconds.
After committing an offensive flagrant foul that helped Texas take the lead, Dixon converted a difficult left-handed floater with 31 seconds left to lift fourth-ranked Missouri past the Longhorns, 67-66.
Dixon missed just once on the night, scoring 21 points on 9-of-10 shooting, while Phil Pressey and Ricardo Ratliffe added 13 points apiece for the Tigers (20-2, 7-2 Big 12), who claimed their second straight victory.
J'Covan Brown led Texas (13-9, 3-6) with 20 points, while Julien Lewis donated 12 points and Myck Kabongo 10 in defeat.
Missouri's double-digit lead trickled away in the final minutes.
Ratliffe and Clint Chapman exchanged easy baskets before a crucial call with just over one minute to play. Dixon caught the ball close to the halfcourt line, and in an attempt to create room, elbowed his defender in the face, prompting an offensive flagrant foul against the Tigers guard. Brown made both free throws, then converted on a high-arching bank shot from the left side for a 66-65 lead with 56.9 seconds to go.
Dixon made amends for his error with a difficult floater with the left hand, giving the visitors the lead once again with 31 ticks to play.
Tigers head coach Frank Haith went to a zone out of the timeout, and it lead to Kabongo's forced jumper in the closing seconds as Brown stood on the opposite end of the floor.