The Red Wings entered the game 0-for-15 on the power play this season and added two more failed attempts, but opened the scoring 13 seconds into the second period when Damien Brunner got a 5-on-4 goal off a feed from Henrik Zetterberg.
"That (pass) was perfect," Brunner said. "I finally got some speed going. … He knows that I'm coming there and it was perfect. He beat the defenseman with the pass so it was a perfect pass."
Zetterberg and Brunner combined on 41 goals playing in Switzerland’s National League during the lockout.
"Today he got a huge goal and got us going," Zetterberg said. "I think it’s good to have some chemistry, but that was a different league, a different ice surface. It will take a little time to adjust here, but hopefully we can keep playing like we did tonight."
The Red Wings scored the final two goals of the second period -- by Zetterberg and Pavel Datsyuk, on a power play -- before Bertuzzi's second of the game gave Detroit a 5-2 lead 4:18 into the third period.
The goals were the first of the season for Bertuzzi, who missed the Wings' first three games with the flu, and Zetterberg. The five goals were more than the Red Wings had managed while starting their season 1-2-0.
"We just needed a win, man," Bertuzzi said. "We need wins. I don’t think it’s anything other than that. I think our power play kind of got us going and it’s a momentum-builder, and it’s also a drainer when it’s not going, so I thought the first unit did a really nice job of getting it going."
Harding, who shut out the Dallas Stars 1-0 on Jan. 20 in his first start since his offseason diagnosis of multiple sclerosis, allowed four goals on the first 17 shots he faced and finished with 22 saves.
"You're looking at the goals, which one could you fault him on?" Wild coach Mike Yeo said. "There are times the puck goes in the net and there's nothing you can do."
Parise's second goal of the game closed the scoring at 10:18 of the third period. The crowd of 20,066 booed him and defenseman Ryan Suter throughout the game; the pair signed with Minnesota rather than Detroit as free agents during the offseason.
Suter, who played 32:02, and rookie Jonas Brodin, making his NHL debut, each had an assist for their first point with the Wild.
Material from team media and wire services was used in this report