The seven-time Super Bowl champion angrily tossed a tablet on the sidelines as both offences struggled to get going, with just a field goal apiece at the end of the third quarter.
Dean struck again in the following drive for the Saints, intercepting Jameis Winston in back-to-back possessions for the Saints and putting the Buccaneers in a solid position on the opposition 29-yard line.
Brady was unable to capitalise, the Buccaneers instead settling on a field goal to extend their lead. The visitors would hold firm despite Michael Thomas giving the Saints hope with a seven-yard touchdown reception.
Having suffered four consecutive regular season losses to the Saints since joining the Buccaneers, Brady's run came to an end, but it was not a vintage performance for the veteran, who completed 18 of 34 attempts for a total of 190 yards.
Tagovailoa shines in comeback victory
Lamar Jackson and the Baltimore Ravens had a fine start against the Miami Dolphins, Devin Duvernay taking the opening kick-off for a 103-yard return and Jackson having three touchdown passes in the first half, as well as a 79-yard rushing touchdown.
When Jackson completed a 75-yard touchdown pass to Rashod Bateman, he became the first quarterback in NFL history to have 75-yard passing and rushing touchdowns in the same game.
Trailing by 21 points heading into the fourth quarter, Tua Tagovailoa threw four touchdown passes to secure a remarkable 42-38 comeback victory – finishing the game with six touchdown passes and 469 yards, completing 36 of 50 attempts.
Jets stun Browns with huge comeback
Victory for the Cleveland Browns at home against the New Yorks Jets would have secured a 2-0 record to start a season for the first time since 1993, and Kevin Stefanski's side looked to be set for a historic win, leading by two scores heading into the final stages.
Nick Chubb had starred with three touchdowns, totalling 87 yards from 17 carries, putting the Browns on the brink, but the Jets responded valiantly to score two touchdowns inside the two-minute warning.