The wild offensive duel, featuring five touchdown passes by Baylor's Robert Griffin, was not decided until Mike Hicks intercepted a pass by TCU quarterback Casey Pachall at the Bears' 18-yard line with 2 seconds to play. A completion in that situation would have allowed the Horned Frogs to line up for a potential game-winning field goal.
TCU had a 13-game winning streak snapped. The Horned Frogs went unbeaten last year en route to a No. 2 national ranking and a Rose Bowl win.
The teams combined for 1,030 yards and produced 50 points in the game's first 19 minutes.
Baylor held a 47-23 lead heading into the fourth quarter but Pachall threw three touchdown passes in the period, ran for one two-point conversion and passed for another.
All that brought the Horned Frogs within 47-45 and they then took the lead with 4:27 to play on a 27-yard field goal by Ross Evans.
Griffin proceeded to drive the Bears 60 yards in 10 plays before Jones kicked his game-winning field goal.
Griffin completed 21-of-27 passes for 359 yards without an interception. He also ran 10 times for 38 yards.
Pachall was 25-of-39 for 251 yards and four touchdowns.