Brust put in 19 points and Gasser added 14 for the Badgers (15-0, 2-0 Big Ten), who outscored Iowa 51-36 during a second half that saw the ejection of Hawkeyes Coach Fran McCaffery for bumping an official.
Iowa was leading 41-39 before the incident, but Wisconsin followed with five points on the ensuing possession to take the lead for good after erasing an 11-point halftime deficit.
At 15-0, the Badgers matched the best start in school history.
Iowa (12-3, 1-1) was led by Roy Devyn Marble with 27 points.
Aaron White added 12 points and eight rebounds.