Brady threw a 17-yard touchdown pass to receiver Kenbrell Thompkins with five seconds left to give the team a 30-27 victory against the Saints.
It was the first loss of the season for the Saints (5-1).
Saints quarterback Drew Brees threw a 34-yard touchdown pass to rookie receiver Kenny Stills with 3:29 remaining in the game on a third-and-20 play to make the score 24-23.
The Saints added a 39-yard field goal by Garrett Hartley with 2:24 left in the game for their final score.
But that just set the stage for Brady to have one of his patented comebacThe game started with what was arguably the Saints worst half of the season.
The Patriots took the opening possession of the game and drove 60 yards to set up a 35-yard field goal by Gostenkowski, which made the score 3-0.
But the Saints came back to take a 7-3 lead in the quarter when Brees threw a 3-yard touchdown pass to Travaris Cadet.
Patriots running back Stevan Ridley then scored two touchdowns in the second quarter to take a 17-7 lead at halftime. Ridley's first score came on a 1-yard touchdown run, which made the score 10-7 with 13 minutes left in the half. The second score came on a 4-yard touchdown run with 7:36 remaining in the half.
The Saints cut the Patriots lead to 17-10 when Hartley hit a 28-yard field goal in the third quarter.
The Saints tied the score in the third quarter when Khiry Robinson ran around left end for a 3-yard touchdown. It was the first touchdown of his career.
But the Patriots (5-1) came back and took a 20-17 lead when Gostenkowski hit a 54-yard field goal with 1:36 remaining in the quarter.