EAST RUTHERFORD, N.J. — Rex and The Sanchise are headed to the playoffs, lucky breaks and all.

Same Old J-E-T-S? Nope, not this time.

Rex Ryan’s top-ranked defense shut down the Cincinnati Bengals and rookie Mark Sanchez efficiently led a clock-eating offense as the Jets clinched their first playoff berth in three seasons with a 37-0 victory at the frigid Meadowlands on Sunday night.

Needing a win to keep their season going, and playing in front of their frosted fans braving Arctic conditions, the Jets (9-7) set up a rematch against the Bengals (10-6) in the first round of the playoffs next Saturday at Cincinnati.

“We planned on being here, regardless of who believed in us or didn’t,” Ryan said. “We’re built for this time of year and this is our time.”

Ryan and his players came back onto the field after a few minutes in the locker room, celebrating with a victory lap and high-fiving the few thousand remaining fans.

The win — marked by Ryan getting a Gatorade shower on the sideline — was likely the last game at Giants Stadium and capped a series of favorable twists and turns for the Jets.

New York appeared to be on the outside of the playoff hunt two weeks ago when it lost to Atlanta, and Ryan even mistakenly said his team’s playoff chances were over.

Instead, the Jets defeated previously undefeated Indianapolis last Sunday when Peyton Manning and other Colts stars went to the bench in the second half. Several other teams in playoff contention lost, setting up the Jets’ win-and-in game against the Bengals.

Wide receiver Braylon Edwards boldly told the fans earlier in the week that the Jets wouldn’t lose, and his teammates backed him up big-time.

“I don’t believe we backed into anything, so we’re going to try to prove it,” Ryan said.

It was the Jets’ first shutout at home since beating Pittsburgh 6-0 on Dec. 14, 2003. Green and white confetti filled the sky after the game as fans waved white rally towels with the words “Win And We’re In” in green letters.

Sanchez was 8 for 16 for 63 yards with no turnovers before being replaced by Kellen Clemens late in the fourth quarter with the game in hand. Thomas Jones ran for 78 yards and two touchdowns and do-it-all wide receiver Brad Smith had 92 yards rushing, including a 32-yard TD run, as the Jets set a record for rushing yards in a season.

The Bengals opened with most of their starters — running back Cedric Benson was the only healthy starter to not play — but pulled Carson Palmer early in the third quarter. Palmer was ineffective when he was in, going 1 for 11 for no — yes, zero — yards before J.T. O’Sullivan replaced him.

The Jets ran 24 plays and the Bengals had three, and Cincinnati was outgained 138 yards to 1 in the first quarter. New York had 250 yards at halftime, including 190 on the ground, to 7 for Cincinnati.

Cincinnati fell to 0-11 at Giants Stadium, including 0-8 against the Jets.

The Jets got things started on their first possession when Smith took a direct snap in the TigerCat formation on third-and-7 from the Bengals 42. He took a few steps to his right and then scooted up the middle before being taken down by Leon Hall and Johnathan Joseph at the 1. Jones took the ball over the top and into the end zone to make it 7-0 4:14 into the game.

Jay Feely’s 20-yard field goal 1:31 into the second quarter made it 10-0, capping a 21-play drive that lasted 11:11.

Smith’s 32-yard touchdown run gave the Jets a 17-0 lead with 6:37 left in the half. Smith, lined up at quarterback, took the snap under center and took off, running over linebacker Rashad Jeanty, and zipping into the end zone.

Jerricho Cotchery had a 6-yard run for a score that made it 24-0 with 37 seconds to go in the first half. New York got the ball right back when Palmer’s pass on the next play from scrimmage was intercepted by Dwight Lowery, who ran it back 34 yards before Palmer pushed him out of bounds. Three plays later, Feely kicked a 39-yarder to give the Jets a 27-point halftime lead.

Jones added a 2-yard touchdown run — his team-record 14th rushing — to make it 37-0 with 9:55 left in the game.

The much-anticipated showdown between Cincinnati’s Chad Ochocinco and New York’s Darrelle Revis ended up decidedly in the Jets cornerback’s favor. Ochocinco left the game with an injured left knee without any catches.

Bengals’ stats

Cincinnati 0 0 0 0 — 0

N.Y. Jets 7 20 3 7 — 37

First Quarter

NYJ—Jones 1 run (Feely kick), 10:46.

Second Quarter

NYJ—FG Feely 20, 13:29.

NYJ—B.Smith 32 run (Feely kick), 6:37.

NYJ—Cotchery 6 run (Feely kick), :37.

NYJ—FG Feely 39, :00.

Third Quarter

NYJ—FG Feely 40, 9:47.

Fourth Quarter

NYJ—Jones 2 run (Feely kick), 9:55.

A—79,106.

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Cin NYJ

First downs 5 21

Total Net Yards 72 320

Rushes-yards 18-72 57-257

Passing 0 63

Punt Returns 2-50 4-59

Kickoff Returns 5-150 1-20

Interceptions Ret. 0-0 1-34

Comp-Att-Int 4-19-1 8-16-0

Sacked-Yards Lost 3-31 0-0

Punts 7-39.3 3-43.3

Fumbles-Lost 2-2 0-0

Penalties-Yards 7-44 4-20

Time of Possession 18:46 41:14

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INDIVIDUAL STATISTICS

RUSHING—Cincinnati, L.Johnson 9-38, Scott 6-20, Leonard 1-8, J.Johnson 1-3, O’Sullivan 1-3. N.Y. Jets, B.Smith 4-92, Jones 27-78, Greene 13-62, Woodhead 6-20, Cotchery 1-6, Sanchez 2-2, Richardson 1-0, Clemens 3-(minus 3).

PASSING—Cincinnati, O’Sullivan 3-8-0-31, C.Palmer 1-11-1-0. N.Y. Jets, Sanchez 8-16-0-63.

RECEIVING—Cincinnati, Coles 3-19, Coats 1-12. N.Y. Jets, Cotchery 5-39, Edwards 2-15, Keller 1-9.

MISSED FIELD GOALS—None.