Barclay Goodrow #21 of the Rangers celebrates his third period goal...

Barclay Goodrow #21 of the Rangers celebrates his third period goal with Artemi Panarin #10 while playing the Detroit Red Wings at Little Caesars Arena on November 10, 2022 in Detroit, Michigan. Credit: Getty Images/Gregory Shamus

DETROIT — Winless in their last three games and having blown two-goal leads in the last two, the Rangers went on the road Thursday as a fragile team, one in desperate need of a win.

And with their dads in the stands watching on this two-game Father’s Weekend road trip, they got what they needed and more, exploding for six goals in the third period to turn a tight game into a laugher in an 8-2 win over the Red Wings.

Detroit had beaten the Rangers in overtime Sunday at the Garden.

“I mean, we needed a win tonight in the worst of ways,’’ said Barclay Goodrow, who scored one of those third-period goals and also had two assists. “So after the second period, it’s kind of gut-check time for us. I think it was a time to show the character we have in the will we have.

“And to put together a period like that, it’s kind of huge for our group — huge for, I think, everyone’s confidence. And it’s nice that the dads got to witness a game like that.’’

Adam Fox, Goodrow, Mika Zibanejad, Julien Gauthier, Libor Hajek and Jimmy Vesey broke open what had been a 2-2 game after two periods. The eight goals were a season high.

Igor Shesterkin didn’t have a busy night in net, finishing with 18 saves.

For Zibanejad, who was playing in his 700th NHL game, his third-period goal was his second of the game and only his second of the season in five-on-five situations. Vesey’s goal came while the Rangers were shorthanded.

“I think we really played a full 60 [minutes],’’ Zibanejad said. “And this one is nice.’’

The Rangers (7-5-3) got a boost from the return of defenseman Ryan Lindgren, who had missed two games with an upper-body injury, and Gauthier, who had missed the last game against the Islanders (also with an upper-body injury).

Zibanejad’s first goal at 15:40 of the first period opened the scoring, but the lead didn’t last long.

Detroit tied it on a goal by fourth-line center Joe Veleno at 18:46 and the Red Wings took the lead at 7:33 of the second period on a goal by Lucas Raymond.

The Rangers tied it on a power-play goal by Chris Kreider, who from his usual spot in front of the net deflected in a pass from Artemi Panarin at 10:59 of the second.

Then the Rangers simply blew out the Red Wings in the third.

Fox got the party started with his fourth goal of the season at 6:02. Filip Chytil’s cross-ice pass for Kaapo Kakko got by Kakko but caromed off the boards and came right to Fox in the upper part of the right circle. Fox fired a one-timer past Detroit goalie Ville Husso to give the Rangers a 3-2 lead.

It was the first of four goals by the Rangers in a span of 2 minutes, 57 seconds.

Goodrow, taking a shift at center on the second line in place of Vincent Trocheck, found himself alone in front of the net and called for Panarin to pass it to him. Goodrow took the pass, went to his backhand and scored to make it 4-2 at 7:23.

Then Zibanejad pounced on the rebound of a shot by Vesey and scored to make it 5-2 at 8:13. After a Detroit turnover, Gauthier drove to the net and banged in a pass from Goodrow to make it 6-2 at 8:59.

Hajek, who stayed in the lineup even though Lindgren came back, made it 7-2 when his left-point shot deflected in off a Detroit player’s stick at 12:47.

Then, with Chytil in the penalty box serving a cross-checking penalty, Vesey scored at 16:31 for his second goal of the season. Fox picked up a secondary assist for his 12th of the season.

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