MIAMI GARDENS, Fla. -- After New York Jets wide receiver Robby Anderson caught an 18-yard, first-quarter touchdown pass on Sunday, he jumped into a first-row, end-zone seat and put his feet up at Hard Rock Stadium.

After routing the visiting Dolphins four weeks ago, it looked like New York was making itself at home at Hard Rock, too.

But when Dolphins quarterback Jay Cutler suffered a third-quarter chest injury -- thanks to a hard hit by Jets linebacker Jordan Jenkins -- Matt Moore, the backup that Dolphins fans chanted for last week, came to the rescue.

Moore, facing a two-touchdown, fourth-quarter deficit, rallied Miami to a 31-28 win over the Jets.

"Matt has a knack for playing the game without fear," said Dolphins head coach Adam Gase, who had no further update on Cutler's condition. "(Moore) prepares the right way. He's done this before."

Indeed, Moore led Miami late last season when Ryan Tannehill got hurt, and he did it again on Sunday, completing 13 of 21 passes for 198 yards, two touchdowns and one interception.

"Guys on both sides of the ball feel confident in Matt," Dolphins safety Reshad Jones said. "Guys love him. He brings energy."

But Moore wasn't the only hero for Miami.

Cornerback Bobby McCain made the biggest defensive play of the game, intercepting a Josh McCown pass at the New York 27 with 47 seconds left in the fourth quarter. That set up Dolphins kicker Cody Parkey, who broke a 28-28 tie with a 37-yard game-winning field goal with 26 seconds left.

McCown's interception spoiled a strong overall performance in which he passed for three touchdowns and ran for one. McCown completed 17 of 27 passes for 209 yards and the one interception.

"I don't want to think about it," McCown said of the blown lead by New York. "To get going on the road like we did and then finish like that ... it's frustrating."

In addition to avenging their loss to the Jets (3-4), the Dolphins (4-2) won their third consecutive game, including two straight in which they overcame a deficit of at least 14 points.

New York scored on its opening possession, a five-play 75-yard march. McCown capped the drive with a 29-yard touchdown pass to Jermaine Kearse, who beat rookie cornerback Cordrea Tankersley on a fly pattern.

Miami tied the score on its opening possession, compiling a nearly identical five-play, 75-yard drive that was capped by a 4-yard touchdown pass from Cutler to Jarvis Landry.

The key play was a spectacular 36-yard reception by Kenny Stills, who caught the ball while on his back. The catch was initially called incomplete, but was overruled on review.

Anderson's touchdown put New York ahead 14-7. That drive was kept alive when running back Matt Forte gained 21 yards on a third-and-19 screen pass.

The Dolphins tied the score 14-14 on a 10-play, 70-yard drive, capped by a 4-yard touchdown pass to tight end Anthony Fasano. The drive was kept alive by a third-down, 28-yard pass-interference call on Buster Skrine.

New York closed the first-half scoring on a 1-yard quarterback sneak by McCown. The two-play, one-yard drive was set up by New York's defense. Safety Jamal Adams came on a blitz and deflected Cutler's pass. Defensive end Muhammad Wilkerson intercepted the pass and lumbered three yards.

The Jets extended their lead to 28-14 on McCown's 10-yard touchdown pass to tight end Austin Seferian-Jenkins. It was the third straight game in which Seferian-Jenkins has caught a TD pass.

But then Moore got going.

With 11:21 left in the fourth quarter, Moore burned New York's safety blitz, hitting Stills for a 28-yard touchdown pass in the right corner of the end zone.

"My adrenaline was as high as it's been for a long time," Moore said.

Five minutes later, Miami tied the score on a 2-yard pass from Moore to Stills.

McCown then made his big mistake, underthrowing Kearse toward the left sideline on the interception.

"They rotated coverage," McCown said of the Dolphins. "The guy (McCain) was underneath, and I just didn't get enough on the throw."

After the game, Wilkerson could be heard yelling inside the Jets locker room, and "Let's rebound!" was the main message.

"It's frustrating," Jets head coach Todd Bowles said, echoing McCown. "We have to develop a killer instinct."

NOTES: Jets RT Brandon Shell (neck) was injured in the first quarter. He was replaced by Brent Qvale. ... Jets DE Muhammad Wilkerson (shoulder, toe) was active despite not practicing all week. ... Jets RB Bilal Powell (calf) was also active. ... Dolphins All-Pro C Mike Pouncey (concussion) was active despite missing the second half of last week's Atlanta Falcons game due to a concussion. He returned to practice on Friday. ... Dolphins WR DeVante Parker missed his second straight game due to an ankle injury. ... Dolphins CB Byron Maxwell, who began the season as a starter, was made inactive for the fourth straight game, even though he practiced fully all week. ... Dolphins DT Vincent Taylor was also a healthy scratch for Miami. The rookie sixth-round pick out of Oklahoma State has played considerably this season, making nine tackles in five games.