Crockett's two free throws with 25 seconds left staved off a late TCU rally, and Hannahs hit 4 of 5 3-pointers.
Jordan Tolbert had 11 points and nine rebounds for the Red Raiders (8-4), who have won three in a row and were playing their first road game of the season. With the win, Chris Walker became the first Texas Tech head coach to win a conference opener on the road in his first season since Dell Morgan in 1933.
Devonta Abron, starting for the first time since Dec. 4, led the Horned Frogs (9-5, 0-1) with 16 points and seven rebounds. TCU had a three-game win streak snapped in its first conference game of its inaugural Big 12 season.