Andrew Copp tied it 1-1 at 7:11, slipping a backhand between Quick’s legs.
Goodrow put New York back ahead 2-1 at 19:31. Vesey’s shot was blocked, but Goodrow knocked the loose puck past Lyon.
Compher tied it 2-2 at 1:24 of the second period when Jeff Petry’s shot deflected off his skate and past Quick.
Larkin gave Detroit a 3-2 lead with a power-play goal at 13:19. Perron’s shot beat Quick and hit the post, but the Rangers goalie lost sight of the puck. Before he could react, Larkin put in the rebound for his 30th goal of the season.
“They are a desperate team,” Quick said. “We know where they are in the standings, and we knew how hard they were going to come out and play.”
Goodrow tied it 3-3 at 13:44 on a rebound for his second of the game.
Kreider’s power-play goal gave the Rangers a 4-3 lead at 10:14 of the third. He scored on the rebound of Mika Zibanejad’s one-timer from the left circle.
“I thought things felt good in the third period,” Lalonde said. “We had some momentum, and then we put their power play out there. They cashed in.”
NOTES: Larkin became the fourth Red Wings player in 30 years to reach 30 goals in three straight seasons, joining Brendan Shanahan (five times), Henrik Zetterberg (four) and Sergei Fedorov (three). … Rangers forward Artemi Panarin had an assist to extend his point streak to eight games (17 points; seven goals, 10 assists).