Detroit finished 1-for-5 with 16 shots on goal on the power play.
"Their best penalty killer was their goaltender," McLellan said.
Said Quinn, "Their power play was humming it pretty good all night long. They generated an awful lot of scoring chances and momentum off of their power play."
Zibanejad tied it 1-1 with a power-play goal of his own at 11:59.
Artemi Panarin's shot from the point was blocked in front by Simon Edvinsson. It also hit Will Cuylle and popped free for Zibanejad, who was already below the left circle. Zibanejad and Panarin each extended their personal point streaks to four games on the play.
The Rangers have scored a power-play goal in four straight games and five of six after scoring four in their first 14 games.
"Our power play doesn't look as good as it did when we weren't scoring, I think there are things we've slipped in, but we're scoring and that's how it goes," Quinn said. "Obviously, we've been more opportunistic."
The goal came 36 seconds after Quick stopped J.T. Compher on a short-handed breakaway.
That was one of 18 saves he made in the second period. Quick made 13 more saves in the third, when Detroit outshot New York 14-3.
But Raymond forced him to go post-to-post and then back to the middle late in the third period. Quick couldn't recover, lost his footing and Raymond scored the game-winner at 16:13.
"The poise and the stick-to-itiveness, that's important, especially when you run into a goaltender that's hot," McLellan said. "We really have been stressing trying to get to the net and make it hard on the goaltenders, and I thought we did that tonight too. I was lucky enough to see (Quick) do that for a lot of years to a lot of teams and you just have to stay with it. Eventually you'll get an opportunity that he can't stop and that was the case tonight."
NOTES: Raymond has 20 points (five goals, 15 assists) in 17 games, the quickest a Red Wings player age 23 or younger has reached 20 points in a season since Sergei Fedorov did it in 12 games in 1993-94. … Dylan Larkin's assist on Raymond's goal was his 599th NHL point. His next goal or assist will make him the 11th player to score at least 600 points with the Red Wings. Panarin's assist was his 305th point at Madison Square Garden, tying him with Steve Vickers for the eighth-most points in the arena. Brian Leetch (543) has the most. … The Rangers had a seven-game winning streak against the Red Wings come to an end.