Rangers goaltender Henrik Lundqvist stops a shot by Red Wings...

Rangers goaltender Henrik Lundqvist stops a shot by Red Wings center Andreas Athanasiou in overtime on Thursday in Detroit. Credit: AP/Paul Sancya

DETROIT — With his team coming off a shutout loss in its previous game and struggling to create offense Thursday night against one of the worst teams in the league, Rangers coach David Quinn didn’t like what he saw on the ice. So he thought to himself, why not change things up?

Said Quinn, “Well, we had had no goals in Dallas and one goal up to that point [Thursday], and I just figured there were some lines I did like and some I didn’t, so I just shook it up.’’

Quinn moved fourth-line wingers Filip Chytil and Boo Nieves up to the flanks of No. 1 center Mika Zibanejad in the third period, creating a radically different look for his team and maybe sending a few messages to some of his other players.

Ultimately, though, the changes weren’t enough to buy the Rangers a win as they fell to the Red Wings, 3-2, in a shootout.

Andreas Athanasiou, who had scored in the third period to give Detroit a 2-1 lead, had the only goal of the shootout, beating Henrik Lundqvist on the second shot of the tiebreaker.

Pavel Buchnevich, who had scored both Rangers goals — the first and last in regulation — was unsuccessful with the final shot of the tiebreaker when he needed to score to keep the shootout going.

Lundqvist, who was playing in his 850th game — he became the 12th goaltender to reach that mark and the third (Martin Brodeur and Tony Esposito are the others) to do it with one team — made 43 saves in regulation and overtime. He was beaten on a deflection by Tyler Bertuzzi in the second period and a four-on-four wrist shot from the hash marks by Athanasiou at 6:15 of the third.

Buchnevich, though, rescued a point for the Rangers (27-28-12) with his backhand goal on a breakaway with 5:31 left in regulation.

The Rangers went 0-1-1 on the road trip, losing two one-goal games. They return home to face the Devils on Saturday.

Quinn decided to elevate Nieves and Chytil to Zibanejad’s line moments before the start of the third period.

“I thought both those guys [Nieves and Chytil] had legs and I thought they were going to put in an effort,’’ Quinn said. “And I thought they did that. That line had some chances and spent time in the offensive zone.’’

“They get tossed on my line at the beginning of the third and I get to know about it right as we’re stepping on the ice,’’ Zibanejad said. “I just tried to gather them — especially young guys not having played a lot of games — I just tried to talk to them and, as a centerman, tried to dictate a little bit and kind of let them know how I play and what I want out of them.

“I’m not asking for anything wild,’’ he said. “I know how they are as players and what kind of players they are, so we just try to jell as fast as you can.’’

Chris Kreider missed a good chunk of the third period before Quinn put him on a line with center Lias Andersson — who had started the game on the fourth line with Nieves and Chytil — and Jimmy Vesey, who had started the game with Zibanejad and Kreider on the first line.

“I thought other guys were playing better, so they’re going to get the ice time,’’ Quinn said when asked about benching Kreider. “Obviously, Chris has had a great year, and [he’ll] get right back at it on Saturday.’’

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