Minnesota (27-6-6) will face North Dakota in the Frozen Four semifinals in Philadelphia on April 10. Boston College will play Union in the other semifinal.
The Gophers are making their third trip to the Frozen Four since winning national titles in 2002 and 2003.
Wilcox, the Big Ten player of the year and a Hobey Baker Award candidate, had his fourth shutout of the season.
Ryan Faragher stopped 12 of 15 shots for the third-seeded Huskies (22-11-5) before he was pulled in favour of freshman Charlie Lindgren, who finished with 19 saves.