MIAMI GARDENS, Fla. — When the Giants landed in South Florida on Sunday afternoon, they quickly fired up their phones and tablets, just as most air travelers would do. They had been in the air for a few of what could have been the most important hours of their season and needed to get caught up on what was happening in the world of the NFC East.

They were on the ground in time to watch Chicago miss a late field goal that gave Washington a win and Buffalo throw a late interception that sealed a win by Philadelphia. The two teams they had been tied with for the lead in the division had pulled ahead of them. And it meant one thing to the Giants.

“Our approach was that this was a playoff game for us,” defensive tackle Cullen Jenkins said. “It’s getting to the point now where we are playing for our season and to keep hope for the division race. For us to know what’s on the line and be able to step up and pull out the win, that’s big.”

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They did just that, earning a much-needed 31-24 victory over the Dolphins on Monday night at SunLife Stadium. The win snapped a three-game losing streak and kept the Giants (6-7) in that logjam at the top of the division.

“It certainly feels good to win and it does keep us alive,” Tom Coughlin said.

To which running back Rashad Jennings said: “You’re doggone right it does.”

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The Giants used a formula that had eluded them all season. They got decent production from their running game (Jennings had 81 yards on 22 carries) and timely defensive stops late, and were able to run out the final 4:39 of the game on offense.

Oh, and they leaned heavily on Eli Manning and Odell Beckham Jr., too. But that should come as no surprise.

Manning completed 27 of 31 passes for 337 yards and threw as many touchdown passes as incompletions (four). Beckham cemented his reputation as the most dazzling receiver in the league with a pair of touchdown receptions, including an 84-yarder that broke a 24-24 tie. His first TD erased a 24-17 third-quarter deficit. He wound up with seven catches for 166 yards.

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Beckham was expected to show off his hands against the Dolphins and former LSU teammate and fellow one-handed catch enthusiast Jarvis Landry. Instead, it was his feet that became the stars.

He caught a 6-yard pass in the end zone on which his toes were blades of grass away from the sideline to tie the score at 24 with 5:01 left in the third quarter. It was so close that the play originally was ruled incomplete and out of bounds, but Coughlin challenged it on Beckham’s urging. The pylon camera used in the ESPN broadcast showed a close-up of Beckham’s toes dragging as he made the grab. The largely pro-Giants crowd in New York’s sixth borough cheered loudly when the replay was shown on the board and when referee Craig Wrolstad made the announcement.

When that drive began, Beckham was in the locker room getting an IV to prevent cramping in the second half. He later scored on an 84-yard slant-and-go pass from Manning, showing off his sprinter’s speed.

“It was a big win,” Manning said. “We knew what happened [Sunday] and we had to stay on track.”

The Giants next face the unbeaten Panthers at home on Sunday and then play the Vikings in Minnesota in a game that has been flexed to prime time — the NFL schedule-maker’s way of calling the Giants relevant — before wrapping up the regular season at home against Philadelphia.

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“Our playoffs started for us already,” Jason Pierre-Paul said. “It’s win or go. We’re not worried about any other team. We’re worried about our team.”

On Monday night, for the first time in a long time, that team looked worthy of a victory and a spot in a playoff hunt.

Coughlin kept saying the Giants would win when they deserved to win.

That it happened when they most needed to win helped, too.

Notes & quotes: TE Will Tye caught a 5-yard touchdown pass with 44 seconds left in the first half that tied the score at 17. It was the first NFL touchdown by a player from Stony Brook University . . . Rueben Randle caught a 6-yard touchdown pass from Manning . . . LT Ereck Flowers (ankle) started but came out in the fourth quarter after aggravating the injury . . . DT Markus Kuhn (knee) and DE George Selvie (concussion) both left the game in the second half . . . DE Damontre Moore, whom the Giants waived Friday, was claimed by the Dolphins. The acquisition will be announced officially Tuesday. Moore was involved in a series of transgressions that culminated in an altercation in the locker room with DT Cullen Jenkins over headphones that Beckham had gifted to teammates . . DE Robert Ayers Jr. (neck) started after missing practice Friday and Saturday . . . S Brandon Meriweather (knee) missed a second straight game.