Playing at home, the Horned Frogs (11-2) had a chance to tie, reaching Boise State's 33-yard line in the final seconds.
But with regular kicker Nick Browne hampered by a pulled quadriceps muscle, Mike Wynn's 51-yard field goal attempt was well short with seven seconds left.
Chris Carr recovered Lonta Hobbs' fumble at the Texas Christian 29 early in the fourth quarter. Dinwiddie gave the Broncos (13-1) a 34-31 lead with an 18-yard touchdown pass to Derek Schouman 2:17 into the final period.
The teams combined for more than 600 yards in the first half, which ended in a 24-24 tie. TCU grabbed a 31-27 lead on Hobbs' seven-yard scamper 5 1/2 minutes into the third quarter.