Couture made it 1-0 52 seconds in, ending a 13-game goal drought that matched the longest of his NHL career (April 4, 2015-Jan. 9, 2016).
"Maybe Al Stalock did me a favor over there," Couture said of the former San Jose goalie. "I texted him before the game, 'I need one buddy.' So maybe he let me get that one. Yeah, it felt good to see that one hit the back of the net."
Timo Meier gave the Sharks a 2-0 lead at 5:55, and Marcus Sorensen made it 3-0 at 16:40.
"We're finding a way as a team to be successful," Meier said. "I want to chip in any way I can. It's great to see we're going in the right direction as a team."
Defenseman Radim Simek scored his first goal in his second game of the season at 18:32 for a 4-0 lead. He had one goal in 41 games last season.
Luke Kunin scored for the Wild at 17:04 of the second period to make it 4-1, but Hertl made it 5-1 at 17:04.
After Staal scored at 17:59 to get Minnesota within 5-2, Evander Kane scored on the power play at 19:15 to make it 6-2.
"We'll take the four points," Kane said. "We did a lot of good things in that game. There were some breakdowns. We got a little too comfortable. We've just got to keep our foot on the gas for a full 60 minutes."
The Wild scored two goals in 1:14 in the third period. Brad Hunt made it 6-3 at 8:07, and Ryan Donato scored his first of the season to make 6-4 at 9:21.
Jason Zucker scored at 15:25 to make it 6-5.
"We had a flurry of emotions to start like that and then end like that, and still not get the reward," Staal said. "We had plenty of chances to tie, we just didn't get it past them. Our first period, I won't make any excuses about it."
Wild defenseman Ryan Suter hit the post with 11 seconds remaining, and Sharks goalie Martin Jones made saves on Zach Parise on a breakaway at 17:38 and on the rebound 17:39.
"We did a lot of good things, but a little too late," Kunin said. "We had some chances."
Jones made 21 saves.
Devan Dubnyk made 17 saves on 19 shots in his 500th NHL game after relieving Stalock to begin the second period.
Minnesota forward Marcus Foligno did not play after the first period because of a lower-body injury.
"I don't know to what extent or anything else," Boudreau said.