"It has truly been a dream come true". But Brees also would have to outpace New England's Tom Brady, who has 500 TD passes, the only active player with more than Brees in that category.
"I don't know if that will ever sink in", Brees added. "Congratulations and I'm proud of you".
On a more serious note, Manning said Brees broke the record "the right way".
In a pre-taped message, Manning said: "All your hard work and dedication has paid off. Congratulations and I'm proud of you".
Mark Ingram had run for touchdowns on one and two yards and Brees flipped a 1-yard touchdown pass to Josh Hill in addition to his record-setting touchdown pass.
Brees is 39 and as insane as it sounds, is probably having the best season of his career.
Brees then removed his helmet, saluted fans and exchanged hugs on the sideline with his wife, Brittany, their four kids and Saints coach Sean Payton.
Brees, who is in his 18th National Football League season, led the Saints to victory in the 2009 season Super Bowl and was the MVP of the game. Five different Saints combined for seven catches of at least 20 yards and New Orleans's 447 total yards were 107 more than Washington had allowed in any of its first three games. Brees surpassed Hall-of-Famer Johnny Unitas' streak of 47 straight - which had stood since 1960. That changed Monday night.
Any hope Washington had of coming back was all but snuffed out when Justin Hardee, a special teams regular who was in the game because of Marshon Lattimore's concussion symptoms, snagged Alex Smith's underthrown pass at the Saints' 19-yard line and returned his first career interception to the Washington 4.
Washington gets a big break in the return of left tackle Trent Williams, who has played like one of the best players at his position leaguewide when healthy.