K'Andre Miller tied it in the third and had an assist, Lafreniere had two assists, and Igor Shesterkin made 25 saves for the Rangers (16-4-1), who were coming off a 5-1 loss to the Buffalo Sabres on Monday.
"That's going to happen during an 82-game season, you're going to have a couple off games, a couple off days," Miller said. "The biggest thing with this group is realizing that we have a really good team and we have a good structure. When everything is going we're usually winning those games. So it's sticking to what we're doing when we're winning those games and trying to play a full 60."
Robby Fabbri had a goal and an assist, Andrew Copp had two assists, and Husso made 38 saves for the Red Wings (11-7-3), who had their three-game winning streak end.
"Unacceptable to not come away with at least one point," Fabbri said. "We were in it. We had the lead for a while. We were playing our game that we played for the last handful of games. We fell asleep there for a couple minutes and that's the result."
Detroit was playing without captain Dylan Larkin (undisclosed injury) for the first time this season. Patrick Kane was a healthy scratch after signing a one-year, $2.75 million contract with the Red Wings on Tuesday.
Shayne Gostisbehere also left the game 2:15 into the third period after the defenseman was hit into the boards by Will Cuylle.
"No update on Shayne," Red Wings coach Derek Lalonde said. "Head. Hit from behind into the boards, and I know the (concussion) spotters pulled him and they were still evaluating him here after (the game)."