Brees became the first player ever with four TD passes, 350 yards passing and a rushing touchdown on Monday Night Football.
The Saints will be under the national spotlight again next week, as the Lions come to town for a Sunday night game. New Orleans is 5-0 at home this year.
Eli Manning completed 33-of-47 passes for 406 yards, two touchdowns and an interception for the Giants (6-5), who have dropped three straight contests and sit one game back of the Cowboys in the NFC East.
With starting running back Ahmad Bradshaw (foot) out for a fourth straight game, Brandon Jacobs carried the ball 13 times for 46 yards and a score. He was limited to just 21 yards last week against the Eagles, while the team had just 29 yards rushing as a team in that game.
Victor Cruz had nine catches for 157 yards and two touchdowns for New York, which arguably has the toughest schedule in the league over the remaining five games -- Green Bay, Dallas twice, Washington and the city-rival Jets.