ATLANTA -- Drew Brees has now completed more passes than any player in NFL history, and he is on pace to set the record for career passing yards in two weeks.

The New Orleans Saints quarterback broke Brett Favre's record with his 6,301st career completion in the second quarter Sunday at Atlanta -- a 17-yard pass to receiver Michael Thomas.

"I hope there's a lot more coming, but I just think about all of the people that had a hand in that," Brees said after the win. "A lot of hands have caught those passes, and a lot of guys have blocked to make those happen. They all are a part of this, absolutely."

He capped another classic performance with a game-winning 1-yard touchdown leap in overtime for a 43-37 overtime victory over the Falcons -- one of the wildest games in the history of this longtime rivalry.

Brees completed 39 of 49 passes for 396 yards and three touchdowns. And he ran for two TDs, the other coming earlier in the fourth quarter when he spun out of a missed tackle by Falcons cornerback Brian Poole for an unlikely 7-yard score.

"At some point, I felt like they were coming to try to take my head off, and I could probably spin out of this. It was just a reaction," said Brees, who joked that it can be a good coaching point for his sons' flag football teams that he coaches. "I keep telling my flag football team that spin moves are good and they're not getting it, they're not believing me. So I'm glad that happened because now I have video evidence to show them that, hey, spin moves work. Spin moves are good."

Brees is now 417 yards away from Peyton Manning's mark of 71,940 career passing yards, which he is on pace to reach on Monday Night Football in Week 5.

Brees, 39, has tried to not make a fuss out of his historic achievements, shrugging off a question about the completions record this past week. But he did acknowledge this summer that the accomplishments are meaningful for not only himself but everyone around the team who was a part of them.

"I try not to think about that," Brees said this offseason. "I'm just trying to think about obviously taking care of business one day at a time. Then when the season rolls around, you take it one week, one game at a time. Eventually those things add up, they stack up, then there you are in a position to do it.

"But there's so many people that are a part of that. There's so many things that come into play with that. I'd rather reflect on that stuff down the road."

Brees is no stranger to making history. He broke Johnny Unitas' record with a touchdown pass in 54 consecutive games from 2009 to '12. He broke Dan Marino's record for single-season passing yards with 5,476 in 2011 (before Manning later passed him). Brees also holds the NFL records for career completion percentage (67.1) and single-season completion percentage (72.0 percent in 2017).

"Drew is the greatest. I'm not saying it because I play with him. He's the greatest," left tackle Terron Armstead said. "How could you dispute? How could you argue he's not the greatest quarterback to ever live? What more does he have to do? Seriously. It's an honor to play with him and to watch him."

Brees' completion percentage is well over 80 this season, too. When asked why he seems to be getting better in that category with age, Brees responded, "I mean, completions are good, right?"

"[It's a result of] trust and confidence in the guys I'm throwing to, getting time to be able to do it with the guys up front. That's everybody working together," Brees said. "Just time on task. Experience, wisdom, treachery. A little bit of all that stuff."