Nick Ritchie scored the deciding goal for the Ducks (29-20-11), who passed the Calgary Flames in the Pacific standings. Calgary hosted the Florida Panthers later Saturday.
WATCH: [All Ducks vs. Wild highlights]
"Anytime you win a shootout that goes that long, you [have to] feel fortunate you got the extra point," Anaheim coach Randy Carlyle said. "There's big stops by our goaltender (John Gibson), and finally found a guy that found the back of the net, Nick Ritchie, five-hole shot, so we'll take it and move on."
The Wild (31-20-7) held a one-point lead over the Flames for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"Every game is big. Every single game I think from here on in is going to be like this," Minnesota coach Bruce Boudreau said. "It's a grind for an awful lot of teams and it's going to be a battle of attrition. I think whichever team can handle it the best is going to succeed."
Ducks forward Ondrej Kase scored the tying goal for the second straight game, at 6:12 of the third period, to make it 2-2.