Gary Harris provided 19 points for the Spartans (15-1, 4-0 Big Ten), who overcame a collapse late in regulation to notch and eighth straight win.
Kenny Kaminski helped out with 15 points.
The Gophers (13-4, 2-2) stormed back from a five-point deficit to force an overtime but then went cold in the extra period, absorbing their first loss in three games.
Andre Hollins netted 24 points and Malik Smith added 17 for Minnesota.
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