EAST RUTHERFORD, N.J. — This was one frantic finish the New York Jets might consider a turning point if they end up pulling off another late-season playoff push.

Mark Sanchez threw a career-high four touchdown passes, including the winning 16-yard score to Santonio Holmes with just over a minute remaining, as the Jets kept pace in the AFC playoff race with a 28-24 comeback victory over the Buffalo Bills on Sunday.

“He’s at his best,” coach Rex Ryan said of his quarterback, “in big moments.”

And, this was certainly one of them. One win down. Five more to go.

With several Jets players saying they needed to win each of their last six games to reach the postseason, things appeared bleak with New York (6-5) trailing 24-21 after Dave Rayner’s 53-yard field goal and facing a third-and-11 from the Bills 36. But Sanchez connected with Plaxico Burress, who reached up and made an impressive one-handed grab along the left sideline for 18 yards and the first down.

“It was crazy,” Jets cornerback Darrelle Revis said of the catch. “He’s 6-foot-5 and he’s got those ‘Go-Go-Gadget’ arms. It was probably one of the best catches I’ve seen in a while.”

Added Sanchez: “I don’t know if words could do it any justice. It was a big-time catch in a crucial situation.”

Sanchez quickly ran a quarterback sneak — just to make sure there was no challenge, even though replays showed Burress caught it cleanly. On the next play, Sanchez rolled out to his right to buy some time and found Holmes alone in the right corner of the end zone to give the Jets the lead with 1:01 left.

“I felt good,” Sanchez said of his confidence entering the winning drive. “We’ve been in that situation before.”

But the Jets then had to overcome a valiant comeback attempt by the Bills (5-6), who have lost four straight. With Buffalo driving for a winning score, a wide-open Stevie Johnson dropped a pass that would have gone for a long gain. Ryan Fitzpatrick also threw behind Johnson in the end zone with 8 seconds left that might have been a touchdown.

“It’s hard,” Fitzpatrick said. “They scored at the end and we had a legitimate four chances to get it in there in the end zone and unfortunately we were unable to make the plays. It hurts real bad.”

Sanchez wasn’t great in this one, going 17 of 35 for 180 yards and an interception, but came through with the game on the line. It was his eighth fourth-quarter comeback victory in two-plus seasons. He also threw two touchdown passes to Dustin Keller and another to Burress as the Jets rebounded from a deflating loss to Tim Tebow and the Denver Broncos 10 days ago.

“Defensively, the one thing we can say is we finished,” Ryan said.

Fitzpatrick was 26 of 39 for 264 yards and three touchdowns, but couldn’t pull out one more in the end. Buffalo played without several injured starters, including Fred Jackson and George Wilson.

Johnson had one of the Bills’ touchdown catches late in the first half and got up and mocked being shot in the thigh, clearly making fun of Burress who served 20 months in prison for shooting himself in the leg in a nightclub in 2008 while he was with the Giants. Johnson then ran to the left side of the end zone mocking the “flight” celebration the Jets often use after scoring and fell to the ground, getting flagged 15 yards for excessive celebration on the play that gave Buffalo a 14-7 lead.

“I was just having fun and part of having fun ended up being a penalty and a touchdown for the Jets,” Johnson said. “It was a stupid decision by myself.”

New York was already going to have good field position, but Rayner flubbed a squibbed kick attempt that hit off the Jets’ Emanuel Cook, who recovered the ball at Buffalo’s 36.

The Jets moved to the 14 when Buffalo’s Marcell Dareus was hit for a 15-yard penalty for using his helmet to make contact with Sanchez. Three plays later, Burress caught a 14-yard touchdown pass in the back of the end zone to tie it at 14 with 1:03 left in the half. Burress simply bowed to the crowd and ran to the stands and handed the ball to his son Elijah, as he always does after scoring receptions.

“I’ve seen worse, and I’ve heard worse,” Burress said of Johnson’s celebration. “So, it doesn’t bother me at all. The result I’m looking at is we won the football game.”

The Jets’ offense started the third quarter with a nice drive capped by Keller’s second touchdown catch of the game that gave New York a 21-14 lead with 3:50 remaining in the period.

After the Jets held the Bills to three-and-out late in the third quarter, Buffalo got the ball right back when cornerback Antonio Cromartie — who was returning the punt because Jim Leonhard was a bit banged up — muffed the fair catch and Leodis McKelvin recovered at New York’s 36. McKelvin injured his ribs on the play and left the game.

Fitzpatrick went for a big play right away, throwing a ball up deep down the right sideline to former Jets wide receiver Brad Smith, who appeared to get a hand on it, along with Cromartie, and tapped the ball up, grabbed it out of the air as the defender fell and took off into the end zone for a career-best 36-yard touchdown that tied it at 21 with 2:11 remaining in the third quarter.

Notes: David Nelson had the Bills’ other touchdown, an 8-yard catch that gave Buffalo a 7-0 lead late in the opening quarter. ... Jets DE Mike DeVito left in the third quarter with a right knee injury, and Ryan had no update on the severity. ... Former Bills first-rounder Aaron Maybin had two of the Jets’ three sacks. He had none in two unproductive seasons in Buffalo. ... Fitzpatrick became the fifth QB in team history with 50 TD passes, joining Jim Kelly, Joe Ferguson, Jack Kemp and Drew Bledsoe.