NEW ORLEANS -- If it were up to No. 1 overall draft pick Jameis Winston, the Tampa Bay Buccaneers quarterback might have burned the videotape of his first NFL start, a two-interception, slap-in-the-face, blowout loss to the Tennessee Titans last week.

However, Winston exhibited an admirable dose of professional amnesia Sunday by calmly throwing for one touchdown and scrambling for another while leading the Buccaneers to a 26-19 victory over the New Orleans Saints at the Mercedes-Benz Superdome.

"Last year we only had two wins, so with this one we are halfway there already," Winston said. "To get a victory on the road, in the division, it's huge for us."

Tampa Bay coach Lovie Smith said of Winston's rocky debut, "Early on, you struggle sometimes. Normally, the biggest improvement that I've seen is from Week 1 to Week 2. We saw a lot of improvement from Jameis and everybody."

Winston exhibited his mental toughness by completing 14 of 21 passes for 207 yards, including a 15-yard scoring strike to wide receiver Vincent Jackson just before halftime that put Tampa Bay (1-1) on top for good, 10-7.

On the play, Jackson beat middle linebacker Stephone Anthony and safety Kenny Phillips down the middle of the field.

"Jameis saw it, and he gave me the right route," Jackson said. "That (middle) linebacker, it's a tough play for him. He has his back to the quarterback. Jameis knows. We work on this play all the time -- put it high in the back, and I'll go over somebody to get it."

With the second-half kickoff, Winston took the Bucs 80 yards in just four plays to expand the Bucs' lead to 17-7. Tampa Bay benefitted from a 40-yard pass-interference call against cornerback Brandon Browner, who was badly beaten by wide receiver Louis Murphy.

Winston got the touchdown by rolling out to the left and then easily running into the end zone from 1 yard out. Bucs coach Lovie Smith said the 14-point swing in a span of 2:10 was the major difference in the game.

"The Saints had scored right before the half, and we needed to answer," Smith said. "Those are the type of drives that give a young quarterback confidence. Plus, we knew we had the ball coming out in the second half. We had to answer."

Tampa Bay's rookie quarterback had all the answers, just as Saints veteran quarterback Drew Brees did not. Brees was sacked four times for 36 yards -- with three of the sacks coming from defensive end Jacquies Smith -- and he appeared to sting his throwing shoulder on the second sack by Smith early in the second quarter.

After the play, Brees continued to rotate his right arm in a circular motion and rub his elbow. Although Brees completed 24 of 38 passes for 255 yards, he displayed difficulty throwing the ball deep and frequently settled for screens or check-down routes.

Asked if he was affected by the hit, Brees replied: "I'd say it affected me on a few of the throws down the field. They just didn't come out very well. ... That's the season. Everybody's dealing with something."

Saints coach Sean Payton said offensive coordinator Pete Carmichael mentioned that Brees took a solid hit to his throwing arm, but he didn't offer any more information on Brees' status.

"When you get in a game where things aren't going well, he's very competitive, very tough," Payton said.

The Bucs extended their lead to 23-7 with field goals of 35 and 22 yards by rookie kicker Kyle Brindza, who also had field goals of 55 and 30 yards and missed only a 52-yard attempt.

The Saints (0-2) cut the deficit to 23-13 with 10:17 left on a 1-yard run by fullback Austin Johnson. Two Bucs fumbles on consecutive series in the fourth quarter gave the Saints a chance to get back in the game. The first, a Winston fumble on a sack, did not result in any points when Zach Hocker missed a 42-yard field goal.

On the next play, Bucs running back Doug Martin fumbled, setting up the Saints at the Tampa Bay 30. Brees completed a 16-yard touchdown pass to Snead to cut it to 23-19 with 7:15 left, but Hocker's extra point was blocked.

The Bucs defense came up with a critical stop on the next series, with safety Chris Conte stripping running back Mark Ingram of the ball on a screen pass, and defensive tackle Henry Melton recovered at the Saints 33.

Brindza gave the Bucs a 26-19 edge by hitting a 30-yard field goal with 1:51 left.

Brees drove the Saints to the Tampa Bay 27, where he had two shots with eight seconds left to get the tying touchdown. His first pass for wide receiver Brandon Coleman was broken up by Conte, and his last was broken up in the back of the end zone.

NOTES: The Saints honored the city for its recovery 10 years after Hurricane Katrina. Former special teams ace Steve Gleason, who is fighting Lou Gehrig's disease, received a standing ovation. ... Bucs C Evan Smith left the game with an ankle injury in the third quarter and did not return. ... Saints RB C.J. Spiller, who missed most of training camp following arthroscopic knee surgery, returned and caught a 19-yard pass on a wheel route on his first play. He added three carries for 7 yards.