Nyquist made two laps of the Senators zone and scored with 48 seconds left in overtime to give the Red Wings a 3-2 win at Canadian Tire Centre.
Nyquist had control of the puck for 28 seconds, fighting off the checks of Senators wing Clarke MacArthur and defenseman Jared Cowen before turning and shooting past goaltender Craig Anderson to give Detroit its first winning streak since Dec. 6-7.
The Senators (14-14-7) have lost three in a row and are 3-4-1 under coach Dave Cameron, who took over from Paul MacLean on Dec. 8.
The Red Wings (19-8-9) came back twice for their second victory in eight games (2-2-4). This was the fifth time in those eight games they went beyond regulation; they lost the previous four in the shootout.
"It was nice to end it in OT this time," Nyquist said. "We haven't been as successful as we want to be in the shootout. We switched it up the last couple of games going with three forwards out there and try and end it in OT. It's nice to see us get the win tonight."
Red Wings coach Mike Babcock said there was no deep thought behind the decision to use three forwards and a defenseman in overtime. Nothing else had worked lately and he said he can put some pretty intimidating quartets together.
"Just tried to win. We weren't winning any of these games, so after doing it for long enough and not winning enough, we changed her up," Babcock said. "I don't know if it's a mental thing or not, when you put [Niklas] Kronwall and [Henrik] Zetterberg and [Pavel] Datsyuk and [Justin] Abdelkader out there together, it looks like four pretty good hockey players to me. That's what we just did. We had three groups of that and we went with that."
Zetterberg had a goal and an assist, and Kronwall had two assists. Abdelkader scored his eighth goal of the season.
Mike Hoffman scored his 11th for the Senators, and MacArthur scored his 10th.
Babcock said the Senators had better legs than the Red Wings after the holiday break, but goaltender Jimmy Howard, playing for the first time in a week after injuring his groin Dec. 19, kept the Red Wings in the game. Howard made 31 saves, including a stop on a breakaway in overtime by Senators captain Erik Karlsson.
"I thought [Howard] was the key for us," Babcock said. "We weren't great. We had turkey legs early, for sure, skating around on two big drumsticks out there and not moving very good. They skated better than us for whatever reason, but our goaltending hung in there and we dug in. We were mentally tough enough in the end to dig in and get mad enough to get her going."
The Red Wings needed three seconds of a penalty to Senators defenseman Mark Borowiecki early in the third period to tie the game 2-2.
With Borowiecki off for interference, Datsyuk won a faceoff straight back from Jean-Gabriel Pageau, the second time the Red Wings won that matchup for a goal.
The puck went to Kronwall, who passed it to Zetterberg at the right point. His shot beat Anderson to the glove side at 3:58.
The Red Wings had a chance to take the lead with Detroit defenseman Jonathan Ericsson in the box when Darren Helm stripped the puck from Karlsson at the Senators blue line and broke in on Anderson. He got his left toe on Helm's backhand attempt.
MacArthur, who said Monday, "I'm cold as a lake trout in the middle of February in Saskatchewan," scored his first goal since Nov. 16 at 13:16 of the second period to put the Senators ahead 2-1.
The Senators played a strong first period and led 1-0 on Mike Hoffman's 11th goal of the season, but the Red Wings tied the game with 14 seconds left.
After Anderson (24 saves) froze the puck with 41 seconds to go, Cameron sent Pageau, a recent call-up from the American Hockey League, out for the faceoff against Datsyuk.
The Red Wings veteran won the draw, and Zetterberg shot wide to Anderson's right. The carom off the end boards was controlled by Abdelkader, who got body position on Cowen and defensemen Cody Ceci in front of the net as the puck came out the other side.
Abdelkader's backhand along the goal line hit Anderson and went into the net.
"A game like this when you've had three days off, it's about surviving," Zetterberg said. "You've just got to survive this game and it won't be pretty. You've just got to try and get the two points and we did that today. [Howard] really kept us in the game. It's great to see him back. It was a nice road win for us."
The Senators had 25 shots through the first two periods but seven in the third.
"In the third we let them off the hook because we got cute," Cameron said. "We stopped shooting the puck. We were trying to make that extra pass, and teams like Detroit they just sit on it. I didn't think we were awful in the third by any means, but they did take it to us because we stopped shooting the puck and we got cute.
"Our pattern has been that we get in trouble when we get cute when we start going east-west as opposed to up and down the rink. For two periods, we were really good going north-south, and in the third we got cute."