The Red Wings blew a 4-1 lead in the third period.
Nyquist had a goal and an assist, Teemu Pulkkinen scored his first career goal, and Jonathan Ericsson and Xavier Ouellet each scored for Detroit. Henrik Zetterberg had three assists to give him seven points in his past two games, and Petr Mrazek made 34 saves to earn the win.
Zach Parise had two goals, Tomas Vanek a goal and an assist, and Mikko Koivu scored for Minnesota. Ryan Suter had two assists.
Devan Dubnyk allowed four goals on 10 shots before being pulled in favor of Darcy Kuemper almost halfway through the game. Kuemper made 14 saves.
Parise's second goal of the game, 19th of the season, tied it 4-4 with 6:39 left in regulation. He intercepted Ericsson's ill-advised pass from behind the Detroit net and jammed his third attempt past Mrazek.
Vanek's ninth goal made it 4-3 with 9:59 left.
Pulkkinen opened the scoring 9:09 into the game when he ripped a one-time slap shot from the high slot off a backhand pass from Stephen Weiss off the rush.
Pulkkinen took his first career penalty a little more than four minutes later, and Minnesota capitalized immediately.
Koivu beat Mrazek with a wrist shot from the right circle with 6:38 left in the first period, seven seconds into the penalty, to tie the game 1-1. It was Koivu's seventh goal.
The Red Wings regained the lead on Ericsson's goal with 5:30 remaining in the opening period. His one-time slap shot from the left point found the short side past Dubnyk's blocker. It was Ericsson's second goal.
Nyquist's power-play goal 3:41 into the second period made it 3-1. He tipped Nilkas Kronwall's shot from the point out of the air and past Dubnyk.
It was Nyquist's 19th goal, 11th on the power play. It was also his third goal in three games.
Ouellet scored his second goal of the season at 7:25. His one-time shot from the high slot deflected up and in off the top of Minnesota forward Justin Fontaine's skate.
Wild coach Mike Yeo then replaced Dubnyk with Kuemper, who had missed the past six games because of a lower-body injury.
Parise pulled Minnesota to within 4-2 with a power-play goal 6:01 into the third period. He put a loose puck into the open side of the net from the bottom of the left circle. It came with Ericsson in the penalty box for high sticking.
Parise has five goals in the past four games.
Mrazek stopped Kyle Brodziak's tip attempt from the lip of the crease 4:27 into the third period.
It was each team's last game before the All-Star break, which ends Jan. 26.