Patrick Maroon also scored for the Ducks, who have won four straight and gotten points in eight consecutive games.
Devin Setoguchi scored a power-play goal for the Wild.
Minnesota got off to a hot start, but couldn't put the Ducks away and saw its four-game home winning streak snapped.
"You have to kind of be honest with yourself. I don't think we played to the standard that we have to play on a nightly basis," Sbisa said. "We weren't happy with the way things were going, but we reacted to it."
The Ducks are the second best team in the Western Conference behind Chicago, but didn't look like it after two periods.
Minnesota got three power-play opportunities in the first and cashed in on the third when Setoguchi scored to make it 1-0.
After a slow start, the Wild have scored a power-play goal in five straight games and seven of their last eight. But the Wild only managed the one goal on five power-play chances Tuesday, and couldn't bury the Ducks while on the man advantage.
Anaheim had prevented Minnesota from scoring during a 5-on-3 advantage earlier in the period.
The Wild thought they had a 1-0 lead 2:27 into the game, but replay officials determined a shot from Torrey Mitchell never crossed the red line. Fans booed the call and Wild players on the bench pointed at the video screen while a replay was shown after the announcement.
"They reviewed it in Toronto, so it's obviously no goal," Mitchell said. "It looked like it crossed the line, but it didn't."
Hiller started in goal for Anaheim after Viktor Fasth sustained an upper-body injury during the morning skate.
Minnesota outshot Anaheim 22-7 after two periods, but only had the one goal thanks to Hiller's strong play. Hiller also was chuckling about surviving an early onslaught of Wild shots in the first period.
"I was hoping we'd come around after those first five minutes. I was hoping," he said. "I know if I can keep a game tight, suddenly things can go your way. We found a way to score. That's what makes this team strong right now. We can win even when we don't play well."
Perry dipped his shoulder and threw an elbow at Zucker's head, sending him crashing into the corner boards. Zucker stayed down on the ice for about five minutes and was helped off by teammates.
The Wild were the better team before the incident, but looked tentative after.
"We looked like a team that was going for the throat to all of a sudden looking like, maybe, wary of what we were losing," Minnesota coach Mike Yeo said. "We have to be able to respond better than that, and responding is what we're going to have to do."
Ducks coach Bruce Boudreau said he only saw the replay of the hit once, as he was heading out for the third period, and he didn't want to comment until he could review it further.
The Ducks tied it 1-1 when Maroon corralled Toni Lydman's shot off the back boards and scored his second goal of the season 3:06 into the third.
It was only Anaheim's ninth shot of the game.
Sbisa scored the go-ahead goal -- his first of the season -- on a shot from the point that deflected past goalie Niklas Backstrom.
The Ducks put 14 shots on goal in the third period, and a smile on Boudreau's face after the game.
"There were a lot of things that went wrong," Boudreau said. "But you kill a 5-on-3 power play, you kill a five-minute major. Then one of your premier players gets kicked out of the game. You already have a whole bunch of young guys in the lineup. To come back and win under those circumstances, I think it's a pretty special character showing by our group."
Fasth's injury forced Anaheim to scramble to make sure it had a backup goalie for the game. The Ducks called on amateur Zach Sikich, a former goalie at the University of St. Thomas in St. Paul, who now runs a goalie school in Minneapolis, to skate with the team during warm-ups while Jeff Deslauriers traveled to Minnesota from Anaheim's ECHL affiliate in Fort Wayne. ... Sikich skated onto the ice behind Hiller, wearing light-blue pads and No. 31. Deslauriers arrived early in the first period and took Sikich's spot on the bench. ... The Wild acquired a sixth-round pick in the 2014 draft from the Ottawa Senators in exchange for forward Matt Kassian. The forward had two career goals and was originally selected by Minnesota in the second round of the 2005 draft.