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, had his fourth shutout of the season.
St. Cloud State finished the season 22-11-5.
BOSTON COLLEGE 4, UMASS-LOWELL 3
WORCESTER, Mass. (AP) — Ian McCoshen scored with 8:44 left and top-seeded Boston College beat UMass-Lowell to reach the Frozen Four for the 11th time in 17 years.
Boston College (28-7-4) is seeking its fourth NCAA championship in seven seasons.
Evan Campbell, Michael Kapla and John Holmstrom scored for UMass-Lowell (26-11-4).