The Longhorns had come back from a 19-point first-half deficit to grab a 33-32 edge with 1:29 remaining on Vondrell McGee's 4-yard touchdown run.
Harrell then worked the Red Raiders down the field and Harrell threw the game-winner to Crabtree, who avoided cornerback Curtis Brown and then tip-toed along the sideline into the end zone.
Harrell connected on 36-of-53 passes for 474 yards with two touchdowns. Edward Britton caught seven passes for 139 yards and Crabtree had 10 receptions for 127 yards for the Red Raiders (9-0, 5-0 Big 12).
Colt McCoy completed 20-of-34 passes for 294 yards with a pair of TDs for Texas (8-1, 4-1).