Josh Doctson broke the TCU record for receiving touchdowns with a pair of scores as the Horned Frogs (5-0, 2-0 Big 12) won their 13th straight game, second nationally to defending champion Ohio State, which took a 17-game streak into its game at Indiana.
The Longhorns (1-4, 0-2), plagued by special-teams mistakes for the third straight game, scored a late touchdown to avoid matching the second-worst shutout loss in school history -- 50-0 to Oklahoma 107 years ago. They are off to their worst start since going 1-9 in 1956.
TCU beat Texas in consecutive years for the first time since 1958-59, outscoring the Longhorns 98-17.
Boykin threw for 332 yards without playing in the fourth quarter, and his 74 career touchdown passes are three more than Cincinnati Bengals quarterback Andy Dalton had from 2007 to 2010.
The Horned Frogs had a 220-1 lead in total yards late in the first quarter after receiver Shaun Nixon threw a 29-yard scoring pass to Doctson on a trick play for a 30-0 lead.
Boykin threw backward to Nixon, and Doctson was well behind Texas cornerback Davante Davis when he caught Nixon's soft toss as he crossed the goal line. It marked the first 30-point quarter against the Longhorns since they gave up 31 in the fourth quarter of a 60-40 loss to Houston in 1987.
Doctson and Turpin each had a flashy score. Doctson soared over Holton Hill on a leaping catch in the back corner of the end zone, and Turpin fooled safety P.J. Locke III with a cut inside from the sideline on a 49-yard score.
Turpin, who had six catches for 138 yards, also had a 50-yard score to put TCU up 37-0 at halftime. His other scores were from 13 and 12 yards as he set a Big 12 record for receiving touchdowns by a freshman.
After special-teams mistakes cost them chances to win late in losses to California and Oklahoma State, the Longhorns buried themselves with early blunders.
On the ensuing free kick, Nick Rose's kickoff went out of bounds, giving the Horned Frogs the ball at the 50. Five plays later, TCU went up 16-0 on a 15-yard pass to Doctson, who had seven catches for 129 yards. His 23 career touchdowns are one more than Josh Boyce had from 2010 to 2012.
A TCU defense missing six starters because of injuries and other issues slowed Jerrod Heard for the second straight week after two explosive games from the Texas freshman quarterback.
Heard was 8-of-20 for 48 yards and had 23 yards on 12 carries before getting replaced by former starter Tyrone Swoopes with TCU leading 47-0 in the third quarter.
The Longhorns return to the Dallas area next week for the annual Red River Rivalry against No. 15 Oklahoma.
The Associated Press and ESPN Stats & Information contributed to this report.