NEW ORLEANS -- The Saints have won six consecutive games for the first time since 2011, and the way their attacking, new-look defense is matching strengths with a perennially high-octane offense, things could get very interesting very soon.

In suffocating the Buccaneers 30-10 Sunday at the Mercedes-Benz Superdome, New Orleans (6-2) kept Tampa Bay (2-6) out of the end zone for 53 minutes and held it to 200 yards in total offense and 3.5 yards a play.

The Saints knocked Jameis Winston out of the game late in the first half on a hit by defensive end Alex Okafor that aggravated a right shoulder injury that the Bucs quarterback initially sustained in an Oct. 15 loss to Arizona.

The Saints' six-game winning streak is second-longest in the NFL, one shy of the Philadelphia Eagles' current run of seven straight.

"We're not ready to just send them to the Hall of Fame right yet, but the guys are competing," New Orleans head coach Sean Payton said. "We're getting a lot of production out of this group. It's encouraging, because we're going to need all those guys. But I like the level at which they're competing."

Rookie running back Alvin Kamara scored two touchdowns and accounted for a career-high 152 yards from scrimmage, and Drew Brees completed 22-of-27 passes for 263 yards and two scores to give the Saints all the offense they needed.

But even Brees -- who for the last three 7-9, non-playoff seasons has had to try to win games on his own -- knows how the Saints' marauding defense is setting the table.

"We feel the energy, we feel the momentum obviously on those third downs when the fans are (screaming for the) defense and they've got the noise meter going," Brees said. "The fans are getting crazy and we're getting (the other team) off the field and the offense is getting the ball and going down and getting points. A lot of good things are happening."

Winston finished 7-of-13 passing for 67 yards, and his longest pass went for 14 yards. Ryan Fitzpatrick replaced Winston in the second half, but he could not generate any offense. The Saints outgained the Bucs 407-200. Tampa Bay lost its fifth consecutive game.

Tampa Bay head coach Dirk Koetter said Winston had X-rays on his sore shoulder after the game to see if the injury was an aggravation of the existing sprained AC joint or a new development. The test results were unknown after the game.

Kamara scored on a 33-yard screen pass and a 6-yard run, and he finished with 84 yards on six receptions and 68 yards rushing on 10 carries. Brees also threw a 36-yard touchdown pass to Ted Ginn Jr. early in the third quarter as New Orleans took a 30-3 lead.

Tensions ran high in the third quarter when Winston, already out of the game, pushed Saints cornerback Marshon Lattimore in the back with his left hand. When Lattimore turned around, Tampa Bay receiver Mike Evans took a running start and slammed into Lattimore from behind, sparking a brief brawl. Evans was given an unsportsmanlike conduct penalty, but stayed in the game.

"I know it went to (replay officials in) New York," Payton said. "If there's not an ejection in that situation, then I don't know when there's supposed to be an ejection."

Koetter said he did not see what transpired during the brawl, but was briefed by team officials on what Evans did.

"That definitely is not the way we want to represent ourselves if it, in fact, was the way I was told," Koetter said. "We're just not good enough in any phase right now."

Asked if he was embarrassed by the way the Bucs are playing, Koetter said: "I would hope so. I'm totally embarrassed by it, and I would hope the players are."

The Saints broke on top with a 40-yard field goal by Wil Lutz and then widened their lead to 9-0 when rookie cornerback Justin Hardee exploded through the middle of the Bucs' punt blocking team to easily block Bryan Anger's punt at the Tampa Bay 20. The ball bounced high into the air and directly into Hardee's arms at the 7-yard line, and he raced in untouched.

NOTES: Tampa Bay DE William Gholston was carted off the field with a neck injury in the third quarter. Head coach Dirk Koetter said Gholston was at a New Orleans hospital being tested for potential problems, but reportedly was "neurologically sound."... Steve Gleason, who made the most famous punt block in Saints history when he broke through to block an Atlanta Falcons punt in the Saints' first game back in the Superdome after Hurricane Katrina, tweeted after the first-quarter punt block by rookie CB Justin Hardee: "#neverpunt BUCS." ... The Saints' defense allowed an average of 32.5 points in losing the season's first two games and just 15.0 points per game during the six-game winning streak. ... Until a late 8-yard touchdown pass from Ryan Fitzpatrick to TE Luke Stocker with 6:48 left, the Bucs had been held out of the end zone for seven consecutive quarters.