Brees also rushed for a touchdown in a dominating performance that enabled the Saints (8-3) to take their third straight win and remain one game ahead of Atlanta in the NFC South standings.
The Saints improved to 5-0 at the Superdome.
Eli Manning went 33-of-47 through the air for 406 yards, two touchdowns and an interception, but it wasn't enough as the Giants (6-5) lost their third straight contest.
Victor Cruz made nine grabs for 157 yards and two touchdowns for New York, which fell one game behind Dallas in the NFC East.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys