The Badgers (14-6, 5-2 Big Ten) only hung on to win when Minnesota's Rodney Williams missed a potential game-tying free throw with 1.6 seconds remaining.
Jackson finished with nine points and Ryan Evans chipped in with 10 and eight rebounds as Wisconsin snapped a two-game skid.
Sam Dekker helped out with 10 points and six boards for the victors.
The Golden Gophers (15-5, 3-4), meanwhile, dropped their fourth straight despite 20 points and five rebounds from Andre Hollins.
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