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ATLANTA -- On the day he became the NFL's career leader in completed passes, Drew Brees' biggest plays came as a runner.

Brees' 1-yard run capped an 80-yard touchdown drive to open overtime that lifted the New Orleans Saints to a 43-37 win over the Atlanta Falcons on Sunday.

That came after his 7-yard score late in the fourth quarter forced the overtime. After the Saints won the coin toss, Brees and the Saints held the ball for more than seven minutes.

Brees jumped over the pile on a quarterback keeper after his apparent 3-yard TD pass to Alvin Kamara was overturned. A review determined Kamara's knee was down before he crossed the goal line. Brees scored on the following play, giving the Saints (2-1) the win.

"This was a wild one," said Brees, who passed for 396 yards and three touchdowns and ran for two scores. Kamara had 15 catches for 124 yards and ran for 66 yards.

Brees' biggest play before the winner might have been his improbable 7-yard scoring run with 1:15 remaining that forced overtime. He ran to his left and then spun to avoid tackle attempts by Brian Poole and Robert Alford.

"At some point, I felt they were coming to take my head off and I could probably spin out of it," Brees said, adding he now has film evidence to show the youth flag football team he coaches that "spin moves work. Spin moves are good."

With his 14th completed pass, the 39-year-old Brees broke the record of 6,300 career completions set by Hall of Famer Brett Favre. Brees set the mark with a 17-yard pass to Michael Thomas in the second quarter.

"I'm just very grateful," Brees said. "I hope there's a lot more coming. I just think about all the people who have had a hand in that. A lot of hands have caught a lot of passes. ... They are all a part of this."

Atlanta's Matt Ryan had his first career game with five scoring passes. Calvin Ridley became the first Atlanta rookie with three scoring catches. That wasn't enough for the Falcons (1-2) against Brees and the high-scoring Saints, who gained 534 yards.

Ryan bemoaned a lost opportunity when the Falcons were forced to punt when stopped at the Atlanta 44 with 25 seconds remaining in overtime.

"We had chances to finish the game today and we didn't do that," Ryan said. "That's disappointing."

Saints coach Sean Payton called the defensive stop "a huge part of the win."

Ryan passed for 374 yards, including 146 to Ridley, who had seven receptions, including a 75-yard TD.

Ridley's third scoring catch against the Saints was a 9-yarder early in the third quarter that held up following a review.

Ryan's five touchdown passes tied the team record set by Wade Wilson on Dec. 13, 1992, at Tampa Bay.

The fifth scoring pass to Mohamed Sanu came after Saints defensive tackle David Onyemata was called for unnecessary roughness on Matt Bryant's 29-yard field goal. With the penalty, the Falcons' offense came back on the field.

Ridley beat P.J. Williams on his first two scoring catches, an 18-yarder in the first quarter and the 75-yarder in the second quarter.

The Saints made a defensive switch, moving Ken Crawley into coverage on Ridley. Crawley was called for pass interference on a deep incompletion to Ridley early in the third quarter that gave Atlanta a first down at the New Orleans 5. On second down from the 9, Ridley's third scoring catch gave the Falcons a 21-16 lead.

Brees completed his first four passes, including a 19-yard scoring pass to Ted Ginn Jr. on the Saints' opening drive.

INJURY REPORT

Saints reserve cornerback Patrick Robinson was carted from the field early in the third quarter with a left ankle injury. He did not return.

Falcons safety Ricardo Allen left early in overtime with a left calf injury. He was helped to the sideline and then driven on a cart to the locker room. ... Reserve cornerback Justin Bethel injured a knee in the third quarter. ... Atlanta rookie linebacker Foyesade Oluokun left in the fourth quarter with an ankle injury.

THOMAS THRIVING

Thomas had 10 catches for 129 yards. His 38 catches are the most by an NFL player in his team's first three games to start a season. His 28 catches through two games also were a record.

PASSING MONTANA

Ryan's 75-yard scoring pass to Ridley was his 34th career TD pass against the Saints, the most by any quarterback. He surpassed Joe Montana's 33 TD passes against New Orleans. Ryan added three more, leaving his total at 37.

DROPS FOR GINN

Ginn dropped a sideline pass on a second-quarter drive that ended with a 49-yard field goal by Will Lutz bouncing off the left upright and over the cross bar. Later in the quarter, Ginn juggled a pass for an incompletion as he ran out of bounds on the Atlanta sideline. He finished with three catches for 12 yards.

UP NEXT

Saints: at New York Giants next Sunday.

Falcons: Play their third straight home game against the Cincinnati Bengals next Sunday.

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