The victory lifted the Jets to 3-3 and dropped Miami to 0-5.
"We needed a win in the worst way," Jets coach Rex Ryan told reporters. "I'm just happy we found a way to get one."
Neither team showed much firepower. The biggest play of the game was turned in by New York's All-Pro cornerback Darrelle Revis who intercepted an errant pass by Dolphins quarterback Matt Moore at the goal line and ran it back 100 yards for a touchdown in the first quarter.
The Jets, who gained a total of 10 yards on nine plays in the first quarter without a first down, finally found their rhythm and scored on a long touchdown drive on their last possession of the first half when quarterback Mark Sanchez ran the ball in from five yards out.
Miami were more efficient than New York in the first half, but stalled each time they got close to the end zone, settling for field goals of 23 and 21 yards.
Sanchez later connected with Santonio Holmes on a 38-yard catch-and-run touchdown in the fourth quarter, and Revis registered another interception to end a last Dolphins' scoring bid.
"It feels great," Sanchez said about ending the slide. "That's just what we needed to get back on track."
Sanchez, picking up steam as the game progressed, completed 14-of-25 passes for 201 yards, while the running attack led by Shonn Greene's 74 yards totalled 104 yards.
Moore connected on 16-of-34 throws with two interceptions and later admitted to frustration over the Dolphins' continuing problem scoring touchdowns in the red zone.
"It's rough. It's the same old story. We're trying to find answers or make plays down there and we seem to be hitting a wall."
The Miami quarterback gave Revis a surprisingly heavy workout.
While most teams direct their air strikes away from the top flight cornerback, Moore kept throwing to his top receiver Brandon Marshall, who was being covered one-on-one by Revis.
Marshall caught six of 13 passes thrown his way, but Revis snared one of them, turning the interception into a romp over the entire length of the gridiron.
"Brandon cut in front of me and he kind of tripped a little bit and the ball was right there," explained Revis. "I started running, made one cut, saw daylight and I just kept on running.
"This was key for us. Losing in this business is tough. It leaves a nasty taste in your mouth and we lost three straight. We wanted to get this win."
The leadup to the game showed disharmony in the Jets clubhouse as co-captain Holmes criticised the offensive line for not protecting the quarterback and failing to open holes for the running game. Veteran offensive lineman Brandon Moore hit back, saying Holmes should have kept quiet.
Coach Ryan said he had talked to both players.
"When you've lost three in a row that's tough. We had to get some things off our chest. We're past that thing. We're chasing a much bigger thing than that and we're moving forward," said Ryan, who has taken the team to the AFC title game the last two years and vowed to lead the Jets to the Super Bowl.
"We're like a family. You're going to have disagreements or whatever. You just resolve them and move forward."
The Jets can expect a sterner test next week when they host the San Diego Chargers (4-1), while Miami should have a better chance of getting a win when they entertain Denver (1-4).