The highest scoring club in the league had run dry, and seemed just a few drops above parched.

Going into the second period trailing Carolina by two goals Tuesday night, the Rangers had been scoreless in five-plus periods. The last goal had come at 12:33 of the second period on Friday in Philadelphia, from Kevin Hayes.

But led by Rick Nash, who had an unassisted goal on a dynamic rush 24 seconds into the third period as well as an assist on Jimmy Vesey’s game-winner on the power play at 14:48, the Rangers rallied for three straight goals and a 3-2 win at Madison Square Garden.

“You get behind the 8-ball against a hard-working team, you need some people to come out and take charge,” said coach Alain Vigneault, “and there’s no doubt that Rick tonight was the leader. He made some great defensive plays, and that first shift in the third, when he tied it up (at 2) and his play on the power play.”

On his game-tying 10th goal, which began when he blocked a shot in his own end, sped up ice and lifted a backhander off the post and behind Cam Ward, Nash said: “I stuttered a bit . . . I sensed I had a step on their two d-men and took it to the net. We had a tough first period, you try to create a spark anyway you can. When you’re expected to be one of the top players, you try to do that every night. Some nights it’s there, some nights it’s not. But I know that’s part of my game, I have to help these guys and lift them when things aren’t going right.”

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Vesey, who hadn’t scored in eight games, completed the rally when Nash’s rebound of Brady Skjei’s shot came to him at the right post. “I just tried to get it on net,” he said. “Felt good.”

Defenseman Nick Holden’s third of the year had snapped the scoreless skein when he grabbed Nash’s rebound, skated to the left of the prone Ward and lifted the puck over the goalie at 9:13 of the second to trim the lead to 2-1.

After a lethargic start at home — where the Blueshirts had lost four straight — and former Ranger Viktor Stalberg had scored twice, the Rangers began applying more pressure, but it took a save by Marc Staal to keep the deficit to one goal.

With Henrik Lundqvist (26 saves) down and out of position after a save, Staal dove and swept a loose puck away from the goal line. The Rangers had several chances in the final minutes of the second.

The first Rangers power play came when Jesper Fast was high-sticked by Jay McClement with 11:45 to go in regulation. But the Rangers dropped to 1-for-16 with the man-advantage, with just one shot on Ward.

When Ron Hainsey hooked Ryan McDonagh down at 13:13, he was given another two minutes for unsportsmanlike conduct when he tried to get to the referee but was held off by a linesman.

Vesey’s goal was challenged by ‘Canes coach Bill Peters for a potential offside on Chris Kreider, but after an inconclusive review, it was counted.

The Rangers (16-7-1), who were beaten 3-2 in Raleigh on Oct. 28, expected another tight one, and were right.

“We need to understand that every game is not going to be 4, 5 or 6 goals,” said Lundqvist. “We need to simplify it sometimes. We need to be able to win 3-2.”

After being down 2-0, he said: “We thought, ‘we need the next goal’. In a lot of games, that third goal is going to be a killer. As soon as we scored the first goal, you could feel the momentum change.”