NEW ORLEANS (AP) — A new start with the New Orleans Saints has put ‘‘the shake’’ back in 33-year-old Darren Sharper.

The NFL’s active leader in career interceptions added two more against rookie Mark Sanchez, returning one a club-record 99 yards for a touchdown to help the unbeaten Saints hand the New York Jets their first loss of the season, 24-10 on Sunday.

Sharper’s trademark shoulder-shaking celebrations are becoming a symbol of a defense that can now take credit for leading New Orleans to victory after taking the blame for the Saints’ failure to make the playoffs the past two seasons.

The 12-year veteran’s five interceptions — two of which he has returned for scores — have helped the Saints start 4-0 for the first time since 1993.

‘‘Sharp’s been a great addition,’’ Saints quarterback Drew Brees said. ‘‘You look at his productivity here over the first four games … that’s pretty impressive.’’

Brees added: ‘‘The defense played outstanding once again.’’

The victory ensured the Saints, who have a bye week coming up, would still be unbeaten when they host the New York Giants on Oct. 18. The Giants (4-0) host struggling Oakland next weekend, giving them a good shot at remaining undefeated as well.

The Jets-Saints matchup drew a lot of attention not only because it was the weekend’s only game between unbeaten teams, but also because it pitted a fearsome defense designed by Jets coach Rex Ryan against the Saints’ league-leading offense, driven by Brees’ prolific passing and the creative playcalling of coach Sean Payton.

New York (3-1) stopped the Saints twice on fourth-and-short and held Brees to 190 yards passing and no touchdowns. After averaging 40 points through their first three games, the Saints didn’t score an offensive touchdown until Pierre Thomas barreled in from a yard out with 6:07 left. Yet that was enough for two-touchdown win.

‘‘It’s not about one side of the ball versus the other,’’ Payton said, seemingly annoyed by all the attention given to the matchup of his offense and Ryan’s defense. ‘‘All three phases are needed to win football games and I thought we did that today.’’

One week after rushing for 126 yards and two scores in a victory at Buffalo, Thomas was the Saints’ offensive leader again. He rushed for 86 yards and caught four short passes for 46 yards. The Saints rushed for 153 yards as a team.

‘‘The Saints outplayed us today,’’ Ryan said. ‘‘They forced a lot of turnovers and scored with them. You’ve got to give them a lot of credit. They ran the ball pretty effectively against us as well.’’

In his first loss as a pro, the Jets’ Sanchez completed 14 of 27 passes for 138 yards and was sacked four times. That still might have been good enough if not for his four turnovers. Saints cornerback Randall Gay also intercepted Sanchez inside the final two minutes, allowing New Orleans to run out the clock.

‘‘My mistakes killed us. They absolutely killed us,’’ Sanchez said. ‘‘The defense played well enough to win. That whole game is 10-10 without three interceptions and a fumble. You turn the ball over like that in this league, and you can’t win.’’

While Brees and the Saints’ league-leading offense were held to only three points through the first three quarters, the big plays by New Orleans’ less-heralded defense gave the Saints an early lead.

Sanchez had driven the Jets impressively to the Saints’ 15 early in the second quarter when Sharper anticipated an attempted touchdown pass, picking it off at the 1 and easily running it back for his second long touchdown return of the season to make it 10-0.

‘‘When I caught it, I kind of stopped and just started running real slow because I wanted to see what was around me,’’ Sharper said. ‘‘Then I said, ’Why don’t I turn on the speed a little bit to show people I can still run.’’’

Only two weeks earlier, Sharper had a 97-yard interception for a score at Philadelphia to tie the club record. Sharper now has 10 career TDs on interception returns, leaving him second all-time in that category, two behind retired former Pittsburgh star Rod Woodson.

New Orleans’ next big defensive play came from end Will Smith only moments after the Jets celebrated a remarkable defensive stand of their own that stopped the Saints on four plays from within 2 yards of the goal line. Smith sacked Sanchez in the end zone, forcing a fumble that Remi Ayodele recovered for a touchdown to make it 17-0.

Sanchez may have been to blame for his team’s early deficit, but he returned to march New York 60 yards in 14 plays, setting up Jay Feely’s 38-yard field goal to make it 17-3.

New York pulled to 17-10 on Thomas Jones’ 15-yard touchdown run in the third quarter, capping a drive set up by Reggie Bush’s fumble on the Saints 34.

The Saints’ defense held from there, however, allowing New Orleans to take control with an 11-play, 74-yard touchdown drive.

NOTES: Sharper has 59 career interceptions, ninth most all-time. … Although the Jets got pressure on Brees, they didn’t sack him. … Jets right tackle Damien Woody left in the third quarter with what the team said was a right ankle injury.