The Bucs would strike again a couple drives later as Winston got the touchdown on a keeper and great second effort to break the plane. The Saints tried to run out the clock, but Brees was sacked on third-and-10. He dropped the New Orleans signal caller for a loss of seven on third-and-3 that forced the Saints to give the ball back.
The Buccaneers (4-11) scored on a pair of 1-yard runs, the first by Peyton Barber and the second by quarterback Jameis Winston.
The Bucs came up empty on their next drive but special teams would come up huge as Tampa Bay punted the ball away.
The Saints scored on the longest kickoff return in club history in the first quarter and took a 14-7 lead late in the period, but found itself in a bit of a struggle with Tampa Bay in the third quarter while nursing a 17-13 lead.
Tampa Bay had rallied for a fourth-quarter lead, only to see the Saints grab the lead back.
Saints defensive end Cameron Jordan picked up his 13th sack of the season, on a play that ended the first half.
Are the Bucs making the right move by sticking with Dirk Koetter?
Expectations were high in 2017 and it's tough to fathom how a team with this much talent has stumbled to a 4-11 record thus far. Dirk Koetter will return to coach the Tampa Bay Buccaneers next year, despite the team's losing record this season.
The Bucs got a 42-yard field goal from Patrick Murray with 4:31 remaining, cutting New Orleans' lead to 24-23.
For the Saints, left tackle Terron Armstead (thigh) was inactive.
Tampa Bay Buccaneers quarterback Jameis Winston tossed a 39-yard touchdown pass to rookie wide receiver Chris Godwin with nine seconds remaining - capping a desperation 95-yard drive with no timeouts - to produce a 31-24 victory over the New Orleans Saints on Sunday at Raymond James Stadium.
New Orleans, bidding for a 12-4 regular season finish, faked its first field goal of the season late in the first half on a fourth-and-five play from the Tampa Bay 30-yard line.
New Orleans would not be able to answer and the Bucs won their last game of the season, 31-24.