It was a rematch of last year's season opener, when the Horned Frogs thumped the Tar Heels 48-14 in Kenan Stadium, spoiling Belichick's college-coaching debut.
TCU didn't score again after going up 10-3 on its first two drives. The Horned Frogs were stopped on fourth-and-short deep in Tar Heels territory on their last two drives.
The 74-year-old Belichick, who won six Super Bowls as an NFL head coach, was 4-8 in his college debut with the Tar Heels last year.
"I'm just happy for the players. They've worked really hard," Belichick said. "To have positive results back up that hard work, reinforces it. I think they've been believing in what we're doing, but I think this just gives everybody a little bit more belief and we've just got to keep building."
Last season, North Carolina never had a halftime lead against a Power Four opponent, but went ahead 12-10 on a safety with 1:49 left in the first half of the first major college football game this season. TCU punter John Hoyet Chance kicked the ball out of the back of the end zone after the snap sailed well over his head.
The Tar Heels ran out the final 4:05 after new TCU quarterback Jaden Craig threw an incompletion when rolling left on fourth-and-2 from the 10.
That followed a missed field goal by Burrell on a 13-play drive by the Tar Heels after their defense stuffed Jeremy Payne, who finished with 142 yards rushing, on fourth-and-1 from the 5.
"Looking back now obviously, I wish we had kicked the two field goals, but at the time, it makes sense to try," TCU coach Sonny Dykes said. "When you're not moving the football, you've got to try to get the ball in the end zone."
Edwards, a transfer from Wisconsin, completed 16 of 28 passes. Jordan Shipp had five catches for 71 yards, and Jaylen McGill had the Tar Heels' only TD, on a 9-yard run in the first quarter after they had converted a fourth-and-7.
Craig, who set passing records at Harvard the past three seasons, was 20 of 32 for 175 yards.
North Carolina had 10 points and 141 total yards in the first quarter with new offensive coordinator Bobby Petrino. The Tar Heels scored 10 points in the first quarter only once last year, but never had more yards. They finished with 322 total yards.
TCU had scored at least 30 points in its last 10 season openers, which was the longest active FBS streak. The Horned Frogs had 10 penalties for 95 yards, including the defense jumping offside when UNC had fourth-and-1 with 30 seconds left.
"Once we kind of got settled down a little bit on the outside runs ... we kind of forced him to cut back and those guys did a good job inside," Belichick said about his defensive front. "They hit the quarterback, they didn't really let him step up in the pocket and throw much."
UNC has an open date before its home opener on Sept. 12, when the Tar Heels host East Tennessee State.
- The Associated Press contributed.
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