NEW ORLEANS -- Drew Brees made NFL history again Monday night.

Brees broke Peyton Manning's career touchdown record with a 5-yard pass to tight end Josh Hill midway through the third quarter against the Indianapolis Colts, giving him 540 for his career.

It was the highlight of a monster night from Brees, who also made NFL history by registering a 96.7 completion percentage as the Saints trounced the Colts 34-7.

Brees tied Tom Brady with his 538th career TD thanks to a 15-yard pass to Michael Thomas early in the second quarter. Then he tied Manning's record at 539 with a 21-yard TD throw to Tre'Quan Smith midway through the second quarter.

"Listen, it was special, everything about the night," Brees said. "I don't know how they pick 'em. Monday Night Football, playing the Colts, the team that we won the Super Bowl against 10 years ago. So the whole Super Bowl XLIV team is back for the 10th anniversary. And, obviously, national television, big game, and now that record in the balance, as well. It just kind of makes you shake your head. 'Are you kidding me?'

"I'm not sure how we got here. It just kind of makes your whole life and career flash before your eyes. Because I never thought I would've had a chance to be a part of something like this, and just looking at the entire journey: Nineteen years from five years in San Diego to 14 years here and all the incredible teammates and coaches that I've had the chance to play with and for -- this team right here, who's very special. And, of course, our fan base, the Who Dat nation, everyone in the Dome tonight, everybody watching tonight. Loved ones, my family, my kids here. Both my college roommates, two of my best friends in the world, were here with their kids. Just an incredible night, incredible experience, incredible moment -- to be able to share that with so many people, because all of them are a big part of this."

When asked if he ever could have envisioned these types of records when his career began, Brees said, "I would've thought you were crazy, absolutely crazy."

"It's hard to fully reflect on it because I know there's still work to be done. And my focus is very much on the goals that this team has set for ourselves," said Brees, who also said it was just a coincidence that he was wearing a Michael Jordan logo on his T-shirt after the game. "But when it's all said and done, I think I'll be able to look back even more and just be so appreciative."

The TD record looked to be broken at the end of the first half, but a scoring pass to Smith in the closing seconds was called back due to offensive pass interference. It didn't matter, though. At 7:08 of the third quarter -- on his 20th consecutive completion of the game -- Brees found Hill for the record-breaker.

Brees remained on fire, throwing a fourth TD later in the third quarter, this time a 28-yarder to Taysom Hill.

Saints coach Sean Payton said they jokingly refer to Brees as Benjamin Button, the movie character who aged in reverse.

"He was outstanding tonight. It was efficient. It was impressive. As a playcaller, the sheet looks a lot bigger when he's playing like that and we're blocking like that," said Payton, who said he couldn't even remember Brees' incompletion.

When told that it was a short pass to running back Latavius Murray in the first quarter, Payton joked, "He'll get a minus on that play. We gotta give one minus, right?"

Brees finished the night 29-of-30 passing, a 96.7 completion percentage that broke Philip Rivers' mark (96.55 set last season on 28-of-29 passing) for best ever in the NFL (minimum 20 attempts).

Brees also set a personal record with 22 consecutive completions (he can break the NFL record of 25 consecutive next week), and he completed 12 of 12 passes to Thomas, who finished with 128 yards.

"I feel like I keep taking him for granted," Saints defensive end Cameron Jordan said. "How many records has he broken? He broke two today. He's unbelievable."

Saints left tackle Terron Armstead said he is never surprised by anything Brees does -- even a performance like Monday night's.

"But amazed? Yes. Still amazed, impressed and just a joy to watch and a joy to be a part of," Armstead said. "This guy's 40, and he's just amazing. The best in the business."

Last season, Brees, who turns 41 next month, also broke Manning's record for career passing yards, and he entered Monday night's game with 76,577 yards. The NFL stopped that game for the accomplishment with a brief ceremony that included his family and a representative from the Pro Football Hall of Fame.

This one came with less fanfare -- likely because Brady could overtake the record as early as Saturday. But Brees was recognized on the scoreboard and took time to point to a section of the crowd before hugging coach Sean Payton and several players on the sideline.

Brady, meanwhile, was among many NFL players to take to social media and applaud Brees for his achievement.

Congrats drew!! Couldn't be more deserving. Passing Peyton in anything is an incredible achievement and your records will be tough to beat! But it's worth trying 😉 — Tom Brady (@TomBrady) December 17, 2019

Brees had downplayed the significance of the record this week with the Saints (11-3) in a tight battle for the NFC's top seeds with the Seattle Seahawks (11-3), San Francisco 49ers (11-3), Green Bay Packers (11-3) and Minnesota Vikings (10-4).

"I think, obviously, before the season, you know you are a certain distance away. But then once the season starts, you just focus on winning games and doing what I need to do as a quarterback of this team to put us in the best position to succeed and to win," Brees said this week. "And with that, I guess the statistics come, and maybe they add up. And then all of a sudden, you're close enough to be within striking distance of some of those things. But I'm really not thinking about it."

Thomas, meanwhile, broke his own franchise record of 125 catches in a season, which he set last year. And he remains on pace to break Marvin Harrison's NFL record of 143 catches in a season.

If Brees and Brady both pass Manning, it will be the first time the NFL's top two leaders in career TD passes were active players since Johnny Unitas and Fran Tarkenton in 1973. Since then, Tarkenton, Dan Marino, Brett Favre and Manning have held the record.