Johan Franzen scored two goals and Damien Brunner had his first Stanley Cup playoff goal and two assists for the Red Wings, who survived a third-period collapse with a timely goal from Nyquist.
"We knew we had to get back to playing hard in the overtime, and we did," Nyquist said. "We knew the playoffs were on the line."
Bobby Ryan scored the tying goal with 2:22 left in regulation for the Ducks, who also got goals from captain Ryan Getzlaf and Kyle Palmieri while erasing Detroit's 4-1 lead with a phenomenal surge in the final minutes.
Game 3 is Saturday night at Joe Louis Arena.
Jimmy Howard made 28 saves for Detroit, which silenced the Anaheim crowd with two goals in the first 4:20. Despite their third-period collapse, the Red Wings earned their third victory in four appearances at Honda Center this season.
Justin Abdelkader scored in the opening minute and Pavel Datsyuk had two assists, but the Red Wings also lost rookie defenseman Danny DeKeyser for the season with a broken thumb.
"He's done," coach Mike Babcock said of DeKeyser.
Jonas Hiller stopped 27 shots and Saku Koivu scored for the second-seeded Ducks, who struggled through the first two periods before rallying for a hair-raising third. Ryan and Palmieri both had a goal and an assist in the third, and Koivu added an assist.
"I think we finally settled into a pretty good rhythm there," Ryan said. "We didn't do enough, though. ... We gave them second and third chances to come up with the puck, and they're a team that capitalizes."
But veteran Ducks defenseman Sheldon Souray took a slashing penalty in front of his net with 38 seconds left in regulation, and Nyquist was left unchecked in the left faceoff circle for his goal with just 2 seconds remaining in the power play. The 23-year-old Swede from the University of Maine was in his sixth career playoff game.
Until the final period, Detroit had bounced back impressively from the Ducks' 3-1 series-opening victory. Babcock put veteran Todd Bertuzzi in his lineup for the first time since Feb. 7, replacing Jordin Tootoo, but otherwise kept the same lineup — and the Wings responded with all the poise expected from a team with 22 straight playoff appearances.
Detroit was led by Franzen, the Swedish veteran nicknamed Mule. He scored a gritty power-play goal on a rebound early in the second period, and he came back from getting hit squarely below the belt by a shot at the second-period buzzer to score again early in the third.
Franzen also appeared to be injured late in the game, but Babcock said he thought Franzen would be fine.
While the Wings executed, the Ducks struggled until their electric third-period rally. Game 1 hero Teemu Selanne made an egregious turnover leading to Brunner's goal, and Getzlaf passed up a breakaway shot in the third period for an ill-advised pass on a play that exemplified the Ducks' struggles.
But the Ducks rallied when Getzlaf scored on a wicked backhand shot with his back to the net with 12:10 to play. Palmieri then scored his first career playoff goal moments after a power play ended, firing a short shot that Howard missed with his glove with 7:29 left.
Ryan nearly scored with 5½ minutes to play, but his deflection in front just caught the outside post. He didn't miss on his next chance when Cam Fowler found him driving to the net with a perfect pass for a quick shot past Howard, setting off a deafening celebration.
The Ducks attracted another large, towel-waving crowd to Honda Center after the festive atmosphere in their opener. But many fans weren't yet in their seats when Abdelkader found space near the blue line and beat Hiller with a deceptive wrist shot that might have been tipped just 48 seconds into the game.
NOTES: The 38-year-old Bertuzzi, who skated on the fourth line, missed nearly three months with back pain and nerve problems affecting his right leg, even forcing him to walk with a cane at times. He played in just seven games and was cleared to return late in the regular season, but he didn't suit up while Detroit won four straight to clinch a playoff spot in its final game. ... The Ducks have won the series all nine times in club history after winning the first game, while Detroit has lost its last three series in which it lost Game 1. ... Babcock considered putting veteran Mikael Samuelsson back into the lineup, but held off. The member of the Triple Gold Club — an Olympic gold medal, a world championship and a Stanley Cup title — missed 41 games this season with injuries, but is healthy again.
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