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Lynne Sladky, Associated Press
Miami Dolphins outside linebacker Jason Taylor (99) is carried off the field following an NFL football game against the New York Jets, Sunday, Jan. 1, 2012, in Miami. The Dolphins defeated the Jets 19-17. This was Taylor's last game with the Miami Dolphins as he announced his retirement.

MIAMI — Jason Taylor stood at his 10-yard line, motioning with both arms to coax more noise from the crowd as the Miami Dolphins tried to hang on to a late lead.

It was Taylor's way of waving goodbye.

His penetration on the next play harried Mark Sanchez into an interception that helped seal the victory, and Miami eliminated the New York Jets from playoff contention by winning 19-17 Sunday.

Taylor, the NFL's active sacks leader, played his final game in a 15-year career. He didn't add to his sack total of 139½, but he lined up at tailback for the final two plays as the Dolphins ran out the clock, then was carried off the field.

"It was a good way to end this thing — to beat your No. 1 rivals in your home stadium in your last game," Taylor said during an emotional postgame news conference. "I'm very, very happy and blessed to be where I am."

Taylor provided a rare moment of celebration for the Dolphins (6-10), who completed their third consecutive losing season, their longest such stretch since the 1960s. They fired coach Tony Sparano on Dec. 12 and have begun the search for a successor.

One small consolation: Miami tied the NFL record for most wins after a 0-7 start.

"Obviously, we wanted more Ws," quarterback Matt Moore said. "It's a time to learn from, and there were a lot of mistakes to go back and correct. But there are a lot of positive things as well. It's hard not to feel good after a win, especially against the Jets."

The Jets (8-8) failed to fulfill coach Rex Ryan's pledge to win a Super Bowl title. Mark Sanchez threw three interceptions, and New York gave up six third-down conversions during the Dolphins' 21-play, 94-yard drive for their only touchdown.

The Jets came into the game needing a win along with losses by three other teams to reach the playoffs. Instead, they finished the season with three consecutive defeats, a big step backward for a team that reached the AFC championship game each of the past two years.

Ryan said he didn't regret his guarantee, even if the Jets fell way short.

"I'm always going to chase the Super Bowl," Ryan said. "If you don't, you're going to be a loser. You have to have the guts to go for that."

The Jets again were victims of their own mistakes, with each interception leading to a field goal. They've given up 126 points off turnovers this year, the most in the NFL.

Sanchez's final misfire came at the Miami 10 with 3 minutes left and the Jets trailing 16-10. Reserve linebacker Marvin Mitchell stepped in front of intended receiver Shonn Greene and rumbled 55 yards to set up a field goal.

The 305-pound Starks came away with two interceptions.

"The interceptions obviously were backbreakers," Ryan said.

Taylor, who said Wednesday he would retire at the end of the season, sent the crowd into pandemonium when he scooped up a fumble and scored with 2½ minutes left. However, a replay review negated the turnover, with the officials determining the ball carrier was down before the fumble.

The Jets then scored with 1:15 to go on Sanchez's 10-yard pass to Patrick Turner, but Miami's Brandon Marshall recovered the ensuing onside kick to seal the win. Taylor joined teammates on offense for the final two plays.

"Playing this game was a privilege," Taylor said. "It was so good to me. I'll miss it. I'm the luckiest man in the world. For the last 15 years I've been able to play a kid's game and get paid to do it."

The Dolphins took the lead for good in the fourth quarter with a drive that took 12 minutes and 29 seconds. Moore threw completions to convert all six third downs during the sequence, including on the final play when he hit Charles Clay with a 1-yard touchdown pass.

The drive set franchise records for the number of plays and time of possession.

"I didn't realize how long it was," Moore said. "It was unbelievable, just a great job on everybody's part."

Otherwise, the Dolphins' offense sputtered without 1,000-yard rusher Reggie Bush, who sat out with a right knee injury. Dan Carpenter compensated with field goals of 44, 58, 40 and 44 yards.

The stands were perhaps half full, reflecting the disenchantment of Dolphins fans. Owner Stephen Ross drew jeers when he honored Taylor during a pregame ceremony, and a small plane overhead tugged a banner that called for the firing of general manager Jeff Ireland.

"This whole season was a lesson for us," cornerback Sean Smith said. "On paper, we were a very good team, but you have to prove it every Sunday."

Notes: Miami WR Davone Bess left the game in the fourth quarter with a right knee injury. LB Karlos Dansby departed in the first quarter with a groin injury. G Richie Incognito left in the third period with a neck injury. ... Jets LB David Harris was ruled out in the fourth quarter with a calf injury. ... Taylor's brother-in-law, former Dolphins LB Zach Thomas, was an honorary co-captain. ... Video tributes to Taylor on the scoreboard during the game included one from Dan Marino wearing jersey No. 99. ... The longest previous drive in Dolphins history was 18 plays.