The touchdown pass was the second for Brooks in the final four minutes, as he hit Joe Horn three minutes earlier to get the Saints (6-8) within three at 17-14. Brooks was also sacked seven times, but finished 14-of-21 for 169 yards.
Aaron Stecker opened the game with a 98-yard kickoff return for a TD for New Orleans, which has won back-to-back contests after dropping its previous three to remain in playoff contention in the NFC.
Joey Galloway accounted for both Tampa Bay (5-9) scores -- one on a pass and the other with a 59-yard punt return. Michael Pittman ran for 131 yards on 24 carries, but his fumble with just over three minutes to go set up the winning touchdown.