Both teams missed field goals in the first overtime. Jaden Oberkrom's 37-yard try was wide left, while Bitancurt's 36-yard attempt was blocked. It was Bitancurt's fourth miss of the game.
TCU went on defense first in the second overtime and gave up Bailey's 15th touchdown grab of the season, a West Virginia record.
The Horned Frogs then made good only their only play of the second overtime.
Boyce, who had six catches for 180 yards and two scores, wasn't surprised at the decision to go for two points, saying Patterson called the same play — although it didn't work — in a close win last year at Boise State.
"In these environments you have to go for it," Boyce said.
Boykin finished 12 of 29 for 254 yards and two scores.
"He was getting hit all night," Boyce said. "But to step up like that, as a freshman quarterback, he's going to be great. He's going to be a great player. We just need to get a couple more things tweaked and we're going to be good."
Patterson also noted the beating Boykin took, joking that he's going to let some offensive linemen play quarterback next week "and see how they like that."
Smith wasn't at his best but generated more points than the past two games combined, both blowout losses to No. 20 Texas Tech and No. 3 Kansas State.
TCU forced Smith out of the pocket and he took several hard hits on runs, including being shaken up in the third quarter after landing awkwardly on a third-down rush. He went to the sideline and crouched on both knees momentarily before heading to the bench. He didn't miss a play.
Smith finished 32 of 54 for 260 yards.
Austin also scored on a 43-yard reception in the second quarter. He caught 11 passes for 101 yards.
West Virginia forced a turnover on special teams when Karl Joseph hit TCU's Skye Dawson on a punt return, and the Mountaineers' Nana Kyeremeh recovered at the 9. Shawne Alston, back from missing four games because of a right thigh bruise, scored from 1 yard for a 21-14 halftime lead.
Bitancurt connected on a career-best 52-yard field goal early in the second half. But on West Virginia's next drive, Bitancurt couldn't handle a low snap on a punt. TCU's Dominic Merka picked up the loose ball and went 15 yards for a score to pull the Horned Frogs within 24-21.