One week after looking so out-of-sorts against a winless team, Drew Brees was at his methodical best to beat a pesky division opponent.
He has a touchdown pass in 36 straight games, tying Brett Favre for second place on the all-time NFL list, and also extended his NFL record to 29 games in a row with at least 20 completions.
Josh Freeman, who had won his previous two starts against the Saints, threw a five-yard touchdown pass to Kellen Winslow with 5:33 remaining in the game, but Brees scrambled for 20 yards on 3rd-and-4 and New Orleans sealed the win with John Kasay's second field goal of the day.
Before Winslow's touchdown, the Bucs (4-4) got all of their points on three Connor Barth field goals.
The Saints were blindsided last week by the lowly Rams, who got their first win of the season over the NFC South leaders one week after New Orleans had routed the Colts, 62-7, to set a franchise record for points.
But they have won two of three now since losing to Tampa Bay, 26-20, on the road last month.
The Bucs, who were coming off a bye after losing to the Bears in London two weeks ago, had a four-game division winning streak snapped and fell to 1-3 in their last four games overall.
LeGarrette Blount rushed 13 times for 72 yards in the loss, but also punched a Saints player in the head early in the third quarter for a penalty that forced the Bucs to settle for a field goal after Ronde Barber intercepted Brees.
Kasay clanked a 42-yard field goal off the upright on New Orleans' first possession of the game, but the Saints stopped Tampa Bay on a 4th-and-1 and scored five plays later when Brees found Moore in the left side of the end zone on a three-yard fade pass to tie Favre.
The 66-yard drive was sparked by Sproles' bruising 35-yard run on first down and his 15-yard catch on the next play.
Thomas had a 33-yard run on the next Saints possession and Sproles took a pass 21 yards down the right side for a TD and 14-0 lead in the second quarter.
Barth kicked a 40-yard field goal with 1:39 left in the first half. Dezmon Briscoe had a 46-yard catch on the first play of the 53-yard drive and it took four Saints to tackle him after he cut in from the right sideline.
But Brees was 6-for-7 on a rushed 76-yard drive, spiking the ball with one second left to set up Kasay's 21-yard field goal for a 17-3 halftime lead.
He was intercepted by Barber on the fifth play from scrimmage in the second half, but the Bucs settled for Barth's 48-yard field goal after Blount's 15- yard penalty for hitting a Saints player in the head with an open hand.
Brees went 6-for-7 on the ensuing drive and Thomas busted through the line on 1st-and-goal for a nine-yard touchdown run to make it 24-6 Saints. The Bucs went on a 15-play drive after that, but again looked to Barth for a 25-yarder.
Earlier, Saints cornerback Tracy Porter was carted off the field after injuring his neck on a low tackle on the second play from scrimmage. Porter was placed on a stretcher with his head stabilized after hitting Buccaneers wide receiver Mike Williams in the legs to break up a slant pass.
The Saints said he was transported to a local hospital and checked out OK neurologically.
Favre had TD passes in 36 straight games for the Packers from 2002-04, while Colts legend Johnny Unitas holds the record at 47 games from 1956-60...New Orleans leads the all-time series, 23-17...Sproles has three receiving TDs this season and six overall, including a punt return. He ran for 42 yards, Ivory rushed for 67 and Thomas 66...The Bucs had nine penalties for 80 yards, while the Saints took eight for 63...New Orleans was 5-for-10 on third downs.