"We would have liked to get that extra point in the shootout, but we played a good road game," defenseman Shane O'Brien said.
Off to the best starts in their team histories, the Wild and Ducks entered the game tied with Dallas for the top spot in the conference with 16 points. Dallas lost Friday night, falling 4-3 at home to Detroit.
Anaheim had a full power play in overtime and Minnesota had a 32-second man advantage, forcing both goalies to make big stops.
Giguere robbed Demitra from the slot with 13 seconds remaining -- the Minnesota winger looked upward in disgust after the save.
Fernandez, who faced six shots in overtime, made two key stops on McDonald.
"He made a great save on my first shot and the second I missed a little and shot it into his stomach," McDonald said. "He's a great goaltender and you saw it again in the shootout."
Minnesota, which has allowed 17 goals in 10 games, held the Ducks scoreless in four power-play chances. The Wild have killed off 32 straight penalties.
With the Wild down 2-1 at the start the third period, Kunitz it at 3:53 when he knocked down a clearing attempt and fired a slap shot from the right circle through traffic and past Fernandez.
Fernandez, who has an NHL-best 1.57 goals-against average, finished with 32 saves. Giguere, whose GAA remains 1.81, stopped 31 shots for Anaheim.
Rolston put Minnesota up 2-1 late in the second period with a tremendous individual effort. Finishing a penalty kill, he carried the puck into the Anaheim zone and dumped it into the right corner.
Following the puck, he checked Getzlaf into the boards before heading toward the bench. As Getzlaf circled behind his net, Koivu stripped the puck from him and centered it to Rolston, who fired a low shot past Giguere.
"I was going off the ice for sure," Rolston said. "As soon as I saw him, I just found a little seam there. He surprised the guy behind the net by being there first of all and just laid a nice one to me."
McDonald redirected a pass from Dustin Penner past Fernandez 6:28 into the game to give Anaheim a 1-0 lead.
Minnesota tied it at 15:10 when Nick Schultz tipped a pass from Todd White behind Giguere. It was Schultz's first goal in 28 games.
Rolston has a seven-game scoring streak. ... The game was the first of three straight road games for Anaheim. The Ducks will play Chicago on Saturday night and St. Louis on Monday night. ... Anaheim's Todd Fedoruk went to the locker room after Derek Boogaard dropped him with a punch to the face during a second-period fight. Fedoruk did not return. ... Minnesota center Wes Walz, who missed two games because of a left hip flexor injury, is listed as day-to-day after suffering a leg injury late in the second period.
Copyright by STATS LLC and The Associated Press
Arena: Xcel Energy Center Location: Saint Paul, Minnesota
Referees: Eric Furlatt, Dan Marouelli Linesmen: Ryan Galloway, Jay Sharrers
Attendance: 18,568 (102.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Andy McDonald (3)
Assists: Dustin Penner, Rob Niedermayer
Nick Schultz (1)
Assists: Todd White, Pierre-Marc Bouchard