Goodale's 39-yard attempt went wide right with no time left on the clock, and Boise State (8-1, 3-1 Mountain West) saw its national title hopes evaporate with the miss.
Casey Pachall racked up five TD passes, including a 25-yarder to Brandon Carter with 1:19 remaining, then connected with Josh Boyce for a two-point conversion, handing TCU (8-2, 5-0) its first second-half lead.
Pachall finished 24-of-37 through the air for 473 yards with one interception.
Boyce hauled down five passes for 163 yards and three touchdowns. Carter ended with two scores on four grabs for 119 yards.
Kellen Moore completed 28-of-37 pass attempts for 320 yards and a pair touchdowns in the Broncos' heart-breaking loss.