AP photo by Mark LoMoglio / Dallas Cowboys defensive end DeMarcus Lawrence (90) pressures Tampa Bay Buccaneers quarterback Tom Brady during the first half of Thursday night's NFL 2021 season opener in Tampa, Fla.

TAMPA, Fla. — Tom Brady and the Tampa Bay Buccaneers didn't flinch.

Down one point with 1:24 to go in the first game of the NFL's 2021 season, the reigning Super Bowl champions were confident their 44-year-old quarterback would find a way to win again Thursday night.

It's simply what Brady, who threw for 379 yards and four touchdowns in a 31-29 win over the Dallas Cowboys, does.

"There was no doubt that we're going to win the game with him," coach Bruce Arians said. "It's just who's going to make plays."

With seats in an NFL stadium filled to full capacity for the first time since the start of the coronavirus pandemic, Ryan Succop's 36-yard field goal with two seconds remaining provided the winning points. Brady set it up with a last-minute drive directed on the same field where Tampa Bay became the first team to play a Super Bowl in its home stadium seven months ago, beating the Kansas City Chiefs 31-9.

Thursday marked the 49th winning drive the three-time NFL MVP has led in the fourth quarter or overtime during the regular season. That's third on the league's all-time list behind Peyton Manning (54) and Drew Brees (53), who are both retired.

"There's obviously a lot to clean up," Brady said after finishing 32-of-50 passing with two interceptions.

The Bucs, hoping to become the first team to repeat as champions since Brady led the 2003 and 2004 New England Patriots to consecutive titles, turned the ball over four times.

"We won," Brady said, "but we know it was far from perfect."

For Brady, a seven-time Super Bowl winner, it was the 300th regular-season start in a sparkling 22-year career — a record for a quarterback. The 44-year-old also joined Drew Brees as the only players to throw for 300-plus yards in a game 100 times.

Chris Godwin, Rob Gronkowski and Antonio Brown caught first-half touchdown passes, and the Bucs extended their winning streak to nine games dating to last December. Brady's second touchdown pass of the night to Gronkowski put the Bucs up 28-19. Succop's field goal came after Greg Zuerlein put the Cowboys ahead with a 48-yard field goal with 1:24 to go.

"As I told our guys, I learned a long time ago we don't learn anything more from losing than you do from almost losing, We've got a lot to learn," Arians said. "Obviously not pleased with the start of the game. Loved the finish. Our guys are winners — they're going to finish."

Dak Prescott threw for 403 yards and three touchdowns for Dallas in his first game since a severe injury ankle ended his 2020 season after five games. The sixth-year pro didn't play in the preseason this year after straining his right shoulder early in training camp, and limitations on his throwing weren't lifted until about two weeks before the opener.

"I thought Dak played well," Cowboys coach Mike McCarthy said. "I really like the way our team played, the preparation coming into it. ... We had tough looks, particularly some of the things they did defensively. I thought our guys did a good job adjusting, did a good job distributing the ball on the perimeter."

The Cowboys have never beaten Brady, who improved to 6-0 against them. Five of the victories came during his historic 20-year run with the New England Patriots before signing with the Bucs last year.

Prescott, though — with help from a revamped Dallas defense that forced a fumble and intercepted a pass that glanced off Tampa Bay running back Leonard Fournette's hands to set up a touchdown and field goal — pushed the Bucs to the limit before a mostly mask-less crowd of 65,566.

Ultimately, though, Brady made the Cowboys pay for kicking woes that contributed to Dallas scoring only 16 points in the opening half. In addition to missing a 31-yard field-goal attempt, Zuerlein had a PAT clank off the left upright in the second quarter.

Seven of the Cowboys' first eight possessions either started or ended in Tampa Bay territory, yet Prescott still faced a nine-point deficit before Dallas pulled within 28-26 on Amari Cooper's 21-yard touchdown catch with less than a minute remaining in the third quarter.

Cooper finished with 13 catches for 139 yards, including a 5-yard score in the second quarter. CeeDee Lamb had a 22-yard touchdown catch for the Cowboys, who finished 6-10 last season.

Brady's two interceptions included a desperation pass at the end of the first half. Ronald Jones and Chris Godwin lost fumbles, with the latter preventing the Bucs from putting away the game in the closing minutes.

Brown had five catches for 121 yards, including a 43-yard score before halftime. Godwin had nine catches for 105 yards, but he fumbled at the Dallas 1 to stop a potential clinching drive before Prescott drove the Cowboys to Zuerlein's go-ahead field goal.