Brees was 26 of 32 passing, including first-half TD throws of 14 yards to TreโQuan Smith, 8 yards to Adam Trautman and 12 yards to Sanders, who missed the previous two games while on the COVID-19 list.
Brees regained the league career TD pass lead with 654, three more than the 43-year-old Brady, who had thrown for 17 touchdowns and just one interception over his previous six games.
The Saints intercepted Brady twice in a 34-23 season-opening win, with Janoris Jenkins returning one for a TD.
Jared Cook fumbled at the Bucs 2 with the Saints looking to build on an early 7-0 lead.
The Saints outgained the Bucs 241 yards to 36 up to that point.