Anaheim, which got another shaky performance from Giguere, lost its fourth straight after a six-game winning streak. The Ducks, whose lone goal came from Corey Perry, have scored five goals during the skid.
"We've got to start getting dirty, start getting in high-traffic areas, playing our physical style of game and playing our skating game," defenseman Chris Pronger said. "We're a skating team that has to support one another, and when we don't we've got a lot of holes."
This marked the start of an eight-game, 15-day road trip for the Ducks, who added last season's leading scorer, Teemu Selanne, to the team on Monday. The Finnish Flash, who scored 48 goals last season, has skated with the team for three days but didn't dress for the game.
"It never hurts to get good players," Ducks coach Randy Carlyle said.
Giguere, who dominated the Wild in playoff series in 2003 and 2007, had a rare Minnesota meltdown early in the second period while the Ducks defense collapsed.
Giguere was going down on a slap shot by Rolston, but the puck was deflected by Francois Beauchemin and went into the top corner of the net 82 seconds into the period. It was Rolston's fourth goal in four games.
Gaborik then held the puck on a slow-developing two-on-one with Pavol Demitra, baiting the defense before beating Giguere high on the glove side with a wrist shot 38 seconds later. It was the All-Star's first goal in six games.
"The goals weren't easy to save, but I'm getting paid to make those saves," Giguere said.
Then a one-timer by Koivu from the slot, after a feed from Demitra, eluded Giguere and prompted Carlyle to summon Jonas Hiller -- who beat the Wild 4-2 in Minnesota on Jan. 18.
"He's a great goaltender, and I don't know if they were on top of their game, but I thought we were really on top of our game," Rolston said. "Our skilled players played well, not only offensively, but they did a great job defensively."
Giguere slammed his stick against the post and chucked his blocker into the bench as he angrily left the ice. It was the second straight game the Ducks pulled Giguere before the midpoint.
He stopped 8-of-11 shots in this one, after allowing three goals on 18 shots in 29 minutes last Thursday in a 3-1 loss in Los Angeles. Giguere is 0-4 with an .863 save percentage and 4.77 goals-against average in his last four appearances.
"I probably would have done the same thing," Giguere said. "I'm not mad at Randy, I'm mad at the situation. I'm mad because we've lost four in a row. It starts by me. I've got to do a better job and make sure I give my team a chance to win."
Defending Stanley Cup champion Anaheim lost for the 21st time in regulation, one more than last season.
Bouchard beat Hiller on a breakaway with 4.5 seconds left in the middle period, and Sheppard finished the scoring with 43.8 seconds remaining in the third.
Minnesota entered the night one point ahead of Calgary in the Northwest Division. Vancouver and Colorado are within three points.
"With the second half here, you want to get off to a good start," Backstrom said. "You look at the standings, you can't have a bad game, bad week. You have to be ready after the break. It's always tough to be five, six days without a game, so it's a big challenge for our team. I think we were ready in the first period and we had a good game."
This was the only time in four meetings this season that the home team won. ... Assistant general manager Tom Lynn said Wild left winger Derek Boogaard will be placed on injured reserve Thursday. Boogaard has missed 17 of 20 games with a bad back. ... The line of Perry, Todd Bertuzzi and Ryan Getzlaf was a combined minus-4. They had nine points and were a plus-6 in the teams' last meeting. ... Right winger Mark Parrish returned to the Wild lineup after missing two games with a bruised foot. ... Backstrom is 36-3-3 when leading at any point of a game and 26-0 when ahead after two periods.
Copyright by STATS LLC and The Associated Press
Arena: Xcel Energy Center Location: Saint Paul, Minnesota
Referees: Greg Kimmerly, Michael McGeough Linesmen: Brian Mach, Thor Nelson
Attendance: 18,568 (102.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Brian Rolston (18)
Assists: Pierre-Marc Bouchard, Eric Belanger
Marian Gaborik (26)
Assists: Mark Parrish, Keith Carney
Mikko Koivu (8)
Assists: Pavol Demitra, Martin Skoula
Corey Perry (27)
Assists: Chris Kunitz, Mathieu Schneider
Pierre-Marc Bouchard (11)
Assist: Brian Rolston
James Sheppard (4)
Assists: Brent Burns, Pavol Demitra