ATLANTA -- Dirk Koetter's first season as Tampa Bay Buccaneers coach got off to a good start. Dan Quinn's second year leading the Atlanta Falcons didn't.

Jameis Winston threw four touchdown passes to prevail in a duel with Matt Ryan and Tampa Bay defeated the NFC South-rival Falcons 31-24 on Sunday.

Winston, getting his second season off in memorable fashion, completed 23 of 33 passes for 281 yards, leading the Bucs to four long drives after a sluggish start that included a first-quarter interception.

"It was fun," Winston said. "It's always good to get a division win. All the phases of football we played today were good. This is the way we want to do it with Coach Koetter. He was a good offensive coordinator and he's a good coach."

Ryan was 27 of 39 passing for 334 yards and two touchdowns, but couldn't bring the Falcons all the way back after they fell behind by 18 points in the third quarter.

"We had some opportunities, but we just didn't make the plays," Ryan said of his team getting just one touchdown in four trips to the red zone. "We're disappointed on how it went."

Ryan was sacked three times, while the Falcons didn't get to Winston. Inside linebacker Kwon Alexander had one of the sacks for the Buccaneers and was in on 17 tackles.

The Falcons won their first five games under Quinn a year ago and were 6-1 before a comeback victory by Tampa Bay in Atlanta sent their season spiraling backward.

A bounce back was hoped for this year, but instead the Bucs and Winston beat them for a third straight time in Koetter's first game as a replacement for Lovie Smith.

"Let's do it 15 more times this year," Koetter said of the victory.

Koetter was presented a game ball by one of the stars of the game in the locker room.

"Who do you think? Number 3 (Winston)," Koetter said. "Hey, it's a good day to be a Buc."

Ryan threw a 25-yard touchdown pass to Julio Jones late in the third quarter and connected with Mohamad Sanu for a two-point conversion.

Matt Bryant's third field goal, a 29-yarder with just under five minutes left, drew the Falcons with seven points, but the Bucs ran down the clock before punting and the Falcons couldn't move after getting the ball at their 9-yard line with 1:52 remaining.

Jones, who had four catches for 66 yards, twisted his left ankle in the fourth quarter, but finished the game.

"We definitely have some things to clean up," said Quinn, whose team committed three penalties that allowed the Bucs first downs. "I was disappointed with the fouls and with our tackling."

Winston's 30-yard pass to Austin Seferian-Jenkins in the back of the end zone climaxed a four-play, 75-yard quick strike to start the second half.

The former Heisman Trophy winner then hit Mike Evans in full stride on a 45-yard bomb to complete a 92-yard march that gave the Bucs three touchdowns in as many possessions.

Charles Sims' weave through the Falcons defense for a 23-yard TD after a short pass from Winston with 14 seconds left in the first half put the Bucs in front 17-13 lead and swung the momentum.

"He's one of the most underrated backs in the league," Winston said. "He showed what a guy can do after he catches it when he's paid to run the ball."

Tampa Bay drove 75 yards in 10 plays after the Falcons' could manage just Bryant's second 34-yard field goal after going backwards following a first-and-goal.

Winston was 2 of 7 passing through Desmond Trufant's interception deep in his own territory that set up Ryan's 5-yard TD pass to Sanu late in the first quarter.

Winston, who had missed Evans in the end zone on the Bucs' first possession, was 15 of 17 in the first half following the interception, including 5 of 5 on another 75-yard drive early in the second quarter that ended with a 4-yard TD pass to Brandon Myers.

Rookie second-round pick Roberto Aguayo kicked a 43-yard field goal to start the scoring for the Bucs.

NOTES: Falcons starting DE Brooks Reed hurt a shoulder in the first quarter and had to be helped off again in the fourth. ... Bucs reserve DE Jacquies Smith injured a knee early in the game and didn't return. ... It was the Falcons' 25th and final home opener at the Georgia Dome. Mercedes-Benz Stadium, with a retractable roof, opens next door next season. ... The starters at LB were all new for the Falcons, with 2015 first-round pick Vic Beasley moving from DE to be joined by rookies Deion Jones and De'Vondre Campbell.