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.
Swim Week Miami Beach 2014 [PHOTOS]