"Obviously it was a good, hard-fought win," coach Sean Payton said. "I have a lot of respect for their team and the way they have been playing. We made enough plays on the road in the game to get the win on both sides off the ball. We made enough plays offensively and we were good with the football. We were smart."
The Bucs (6-7) saw their wild-card hopes take a hit as they weren't able to score enough against the NFL's worst defense. Tampa Bay had a chance to tie the game late, but punted rather than try for a first down when facing a fourth-and-10 with 4:21 left.
The Saints (5-8) converted 12 third downs, including two key conversions on their final drive to eat up clock while holding the lead. Brees threw for 312 yards and running back Tim Hightower, filling in for the injured Mark Ingram, rushed for 81 yards and a touchdown.
The Bucs' offense came alive on a fourth-quarter drive, including a conversion on fourth-and-4 on a completion to tight end Austin Seferian-Jenkins. Winston went 7-for-8 for 84 yards on the drive, capped with a 6-yard scoring throw to rookie Adam Humphries to cut the lead to 24-17 with 8:56 left in the game.
"We knew what was at stake today. Normally, you play your best ball when this much is on the line," Tampa Bay coach Lovie Smith said. "It's amazing we lost, but by seven points. You have to give the Saints a lot of credit."
The Saints had jumped out to a 14-0 lead, with Brees completing his first nine passes. Early in the second, he had two touchdown passes to receiver Marques Colston, while completing 12 of 13 passes for 128 yards.
"We are playing for jobs," Saints cornerback Delvin Breaux said. "I think we are out of (the playoffs), but I don't know. The fact that these guys are coming and competing each day -- we knew it was going to swing eventually, and today was a day we got everything swinging for us. It was awesome."
The Bucs had only one first down in their first three drives. They got a spark from three Saints' penalties for 35 yards on one drive, with running back Doug Martin scoring from 14 yards out to cut the lead to 14-7.
The teams would trade field goals in the final two minutes of the half for a 17-10 Saints halftime lead.
"The first half was unfortunate -- first play, explosive, but we get called for holding," quarterback Jameis Winston said. "So that definitely took our momentum ... you know, we have to bounce back. Quick turnaround, we've got the Rams (on the road Thursday) and (must) play better."
The Bucs got the ball with a chance to tie in the third quarter, but Connor Barth missed a 47-yard field goal, and the Saints went 63 yards for a touchdown and a 24-10 lead. Hightower scored the TD on a 3-yard run.
NOTES: Saints RB Tim Hightower, who didn't play a down in the NFL from 2012 through 2014 and had just 48 yards all season, stepped in for the injured Mark Ingram (shoulder) and had 85 yards on 28 carries and what turned out to be the game-winning touchdown late in the third quarter. ... The Saints held Bucs WR Mike Evans without a catch in the first half, and he finished with three catches for 39 yards. "We took him away in this game," Saints coach Sean Payton said. ... Bucs WR Vincent Jackson left the game with a knee injury and did not return. He was limited to one catch for 5 yards. ... WR Willie Snead had a huge game for the Saints, catching seven passes on eight targets for 122 yards, including a 41-yard catch to convert a third-and-21 situation.