TCU (2-0) led 14-7 entering the fourth quarter but scored two late touchdowns in a span of 14 seconds to pull away from the Razorbacks (1-1).
After TCU sophomore running back Darius Anderson ran 14 yards for a touchdown with 2:18 remaining in the game, Arkansas fumbled the ensuing kickoff. TCU took over at the Arkansas 13. On the next play, sophomore running back Sewo Olonilua took a direct snap and ran for his second touchdown of the game.
Jonathan Song's extra point made it 28-7 with 2:04 left.
Arkansas coach Bret Bielema, whose team gave up big leads in its last two games of the 2016 season, was disappointed in the fourth-quarter performance against TCU.
"Since last January, we've emphasized and talked about the way you finish games," Bielema said. "That's not the group I've been working with for the last six months."
TCU, which passed for 300 yards in a 63-0 season-opening victory against Jackson State a week ago, had 166 yards passing against Arkansas. But the Horned Frogs ran for 196 yards, led by 106 yards on 15 carries from Anderson.
Defensively, TCU kept Arkansas' dangerous running attack under control, holding the Razorbacks to 129 yards. David Williams had 65 yards on 10 carries for Arkansas.
"If you had told me going late into the fourth quarter that it was going to be 14-7, I thought we'd have more than that," Bielema said. "But I really think those last two touchdowns were just a little bit of -- they definitely weren't tackling like they were in the first half."
The Horned Frogs held Arkansas without a first down on five of the Razorbacks' 10 possessions. Arkansas punted six times, missed two short field-goal attempts, fumbled a kickoff and lost the ball on downs on its final possession.
"You have to play hard on first down and third down," TCU coach Gary Patterson said. "You've got to get three-and-outs and takeaways."
TCU senior quarterback Kenny Hill completed 21 of 31 attempts for 166 yards with an interception. Arkansas senior Austin Allen was 9 of 23 for 138 yards and a touchdown.
Patterson didn't seem concerned about the relative lack of production in the passing game.
"I've got to watch the film, but any time you win on the road, you come closer to having a complete (team)," Patterson said after the game. "There are a lot of different areas that made the difference today."
TCU took the lead on its opening possession and never trailed.
After a short Arkansas punt, the Horned Frogs drove 45 yards in eight plays, capped by Olonilua's 1-yard touchdown run with 10:43 remaining in the first quarter.
Arkansas answered on the following possession when Allen found junior wide receiver Jonathan Nance for a 49-yard touchdown pass. Cole Hedlund's extra point tied the score 7-7 with 8:15 remaining in the first quarter.
Kyle Hicks' 4-yard touchdown run with 7:39 remaining in the first quarter capped an 80-yard drive in 15 plays, and Song's extra point gave the Horned Frogs a 14-7 lead.