The Badgers (15-1, 3-0 Big Ten) pulled away from a 45-all tie with a 9-2 run to open a 54-47 lead on Gasser's free throw with 3:19 left.
Wisconsin, which has won eight straight since an 80-70 loss at home to Duke in early December, maintained a two-possession lead the rest of the way.
The Badgers offset a 43.6 percent shooting night by making 25 of 31 free throws, including 15 in the final 9:11.
Jon Octeus had 15 points and a team-high eight rebounds for Purdue (10-6, 2-1). A.J. Hammons and Isaac Hass added 11 points apiece. The Boilermakers were trying to become the first Big Ten opponent to win four games at the Kohl Center.
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