Miami Dolphins kicker Dan Carpenter (5) reacts after missing a field goal during overtime of an NFL football game against the New York Jets, Sunday, Sept. 23, 2012, in Miami. The Jets won 23-20. (AP Photo/Wilfredo Lee) Photo: AP

KERLEY HIGH: Jeremy Kerley is hoisted in the air after catching a 7-yard touchdown pass late in the fourth quarter. The Dolphins tied it, but the Jets won it in overtime. (Getty Images)

MIAMI — In honor of Santonio Holmes’ big day, we’ll start with the positive — the Jets defeated the Dolphins 23-20 in overtime and are now in first place in the AFC East.

OK, stop reading Santonio, because it gets negative from here.

The Jets got the win in ugly, ugly fashion in a four-hour slop-fest at Sun Life Stadium. In the process, they may have lost their best player in the process with cornerback Darrelle Revis exiting the game in the third quarter after injuring his left knee. Revis will have an MRI exam today, but it is believed he suffered ligament damage.

Nick Folk’s 33-yard, game-winning field goal with 6:04 left in overtime made the Jets’ poor play more tolerable. Still, they have to be troubled by the deficiencies they showed on both sides of the ball.

“We’ll certainly take the win,” coach Rex Ryan said. “We’re not going to give it back.”

The game-winning drive came after Dolphins kicker Dan Carpenter missed a 48-yard field goal with 8:00 left in the extra period. Folk’s kick was set up by a 38-yard connection between Mark Sanchez and Holmes down the sideline over Miami cornerback Richard Marshall.

Two plays later, the Jets lined up for the 33-yard attempt by Folk on third down. Sun Life Stadium exploded when the Dolphins blocked Folk’s initial attempt, but Dolphins coach Joe Philbin had called timeout just before the kick. On the second try, Folk nailed it, sending the Jets’ sideline into a celebration.

“I saw the guy call a timeout,” linebacker Calvin Pace said. “I wasn’t too much worried about. If it had been really blocked, I think I would have went to a knee and shed a tear. I don’t know how much I had left in me. I was spent in this hot, humid sweatbox.”

It was a day of redemption for Holmes, who tied a career high with nine catches for 147 yards in the same stadium where he was benched last season. It was the first 100-yard game for Holmes since November 2010, a stretch of 27 games.

“I just went out and played Santonio Holmes football,” the wide receiver said. “Sanchez really felt comfortable giving me the ball, putting it in great places. We went out and did what we had to do to steal a victory here in Miami.”

Steal is the appropriate verb.

The Jets’ first drive of the day ended with a Sanchez interception by Marshall. The Dolphins offense then sliced through the Jets D, largely on the back of running back Reggie Bush. They drove 47 yards on eight plays with Daniel Thomas’ 1-yard touchdown giving Miami a 7-0 lead.

Bush had 50 yards rushing in the first quarter. He injured his knee just before halftime, a huge relief to the Jets defense.

Even after playing a terrible first half when they managed just 114 yards, the Jets trailed by only a touchdown at halftime at 10-3.

The defense forced turnovers on the Dolphins’ first two possessions of the second half, with safety LaRon Landry returning a Ryan Tannehill interception for a touchdown to tie the game. Revis recovered a Thomas fumble a play later, setting the Jets up on the Dolphins 26.

The Jets got the ball down to the 2-yard line, when they inserted Tim Tebow, who had a pass-run option on second down and ended up getting tackled for a 5-yard loss. Sanchez topped Tebow’s inept play on third down, lofting a poor pass into the end zone that was intercepted by Chris Clemons.

Sanchez completed just 21-of-45, though he totaled 306 yards.

“There were certain spans during the game where I left too many completions out there,” Sanchez said. “I missed some throws that I can easily make and this team fought and we battled.”

Sanchez and the Jets finally took the lead late in the fourth quarter, when he hit Jeremy Kerley for a 7-yard touchdown on a slant to go up 20-17 with 3:01 left.

Miami again ran through a tired Jets defense and Carpenter tied the game with a 41-yard field goal with 21 seconds to play, forcing the overtime.

After the game, the Jets were not apologizing for the way it looked. With games against the 49ers and Texans next on the schedule, they know how huge this win is.

“It goes down as a W,” guard Brandon Moore said. “We fought to the end. These are guys that are tough to win. Good teams win this game. They close them out and find ways to win when it’s not so pretty.”