Adam Haluska, the Big Ten's leading scorer entering the game, finished with 21 points and Tyler Smith added 17 points and six assists for Iowa (10-8, 2-2), which rallied from a 21-point deficit in the second half to make the game close.
The Hoosiers, who improved to 10-0 at Assembly Hall this season and snapped a four-game losing streak against Iowa, took charge early in the first half following Haluska's layup that put Iowa ahead 10-8.
White's rebound and putback tied the score and sparked an 11-0 run by Indiana over the next seven minutes. Lance Stemler's 3-pointer gave the Hoosiers a 19-10 advantage with 7:30 left.
Indiana extended its lead to 24-13 after White's basket with 6 minutes remaining, and the Hoosiers went up 29-17 on Wilmont's 3-pointer to end the half.
Wilmont made three 3-pointers and scored 11 points, and White added eight points and six rebounds to lead Indiana in the first half. The Hawkeyes shot 32 percent from the field and committed 10 turnovers before the break.
The Hoosiers began the second half with a Bassett 3-pointer and a White layup to take a 34-17 edge.
Iowa cut the deficit to 44-32 following Haluska's basket with 13 minutes left, but Indiana answered with a 12-3 run, which was capped by White's layup to put the Hoosiers ahead 56-35 midway through the second half.
The Hawkeyes made a late rally, closing to within 68-60 after Haluska's layup with 37 seconds left. Indiana then made three free throws down the stretch to seal the victory.