The result means that the Bucs, whose only Super Bowl title came 18 years ago, face the Green Bay Packers in the NFC Championship Game – Brady’s ninth game in 10 seasons.
Meanwhile, defending champions Kansas City Chiefs will face Buffalo Bills in the AFC Championship game.
The Chiefs lost quarterback Patrick Mahomes due to a concussion in the third quarter against the Cleveland Browns on Sunday, but managed a 22-17 victory.
Brees uncertain future
While the Saints led the first exchanges in the Mercedes-Benz Superdome, it was the Bucs’ defense that forced a crucial turn and proved decisive.
Brady’s two touchdown passes were completed by Mike Evans and Leonard Fournette before his own score in the fourth period resolved the game.
“As I said, the offensive line was incredible. It was just a very disputed game, a very physical game.
“We need to rest … and be ready for training on Wednesday.”
For Brees, this could have been the last game of his career with uncertainty about the future of the 42-year-old turning.
He added: “Obviously, it has been fantastic for this team, this city, I could go on indefinitely. But we will wait and respond at the right time.”
‘I will not waver’
In Sunday’s other game, the Chiefs had to call reserve defender Chad Henne to guide the team to victory over the Browns.
Mahomes, last season’s Super Bowl MVP, opened the scoring as he ran for a yard touchdown before meeting Travis Kelce for the second touchdown of the game.
But he was forced to leave the field in the middle of the third quarter due to the concussion protocol, and in the second half the Browns began to close the gap.
“Somewhere you have to be able to go deeper in difficult times and get it,” said Chiefs coach Andy Reid, of how his team reacted after losing Mahomes and held on for the win.
“And if the coaches are retreating, if the players – their leaders – are retreating, it will not happen.
“And our locker room is not going to budge. They are tough like that.”
The Chiefs now face the Bills on January 24 for a spot in the Super Bowl LV.