Brees entered the game needing 201 yards to eclipse Peyton Manning's previous mark of 71,940 yards.
Brees was immediately enveloped by his teammates in a joyful hug, then he pointed to the home crowd while Pro Football Hall of Fame President David Baker took possession of the football used on the play.
The 39-year-old signal caller was honored during a brief stoppage in play after breaking the record, receiving an ovation from players and fans at the Mercedes-Benz Superdome in New Orleans as he huddled with his family and Saints owner Gayle Benson.
In a victory at Atlanta earlier this season, Brees broke Brett Favre's career record of 6,300 completions.
A second-round pick by the Chargers in 2001 after setting records at Purdue, Brees spent five seasons in San Diego as his career got off to a somewhat slow start. He finished the game completing 26 of 29 passes for 363 yards and three touchdowns.
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With the game well in hand after the two-minute warning, Payton subbed Brees out of the game.
"This is one of the great stories in National Football League history - a guy who was told was told every reason why he would never be the guy", Joe Tessitore, the "MNF" announcer, said before the game (via the Advocate).
As you can see, Brees did it in style with a long touchdown connection and, on cue, the sports world opened its arms to congratulate him on what is an awe-inspiring accomplishment. And you've ruined that for me.
"He deserves it. It's been an unbelievable run", Payton said.
Mark Ingram had run for touchdowns of one and two yards and Brees flipped a 1-yard touchdown pass to Josh Hill for other Saints scoring in the first half.
It also took Brees fewer games than Manning to pass for 71,740 yards - Brees achieved the feat in 253 games compared to Manning's 266.