Trailing by four points in the final minutes, Minnesota's Joe Coleman made a layup with 1:47 left, shaving the Golden Gophers' deficit to two.
Iowa's Roy Devyn Marble threw the ball away on the next possession and Hollins then drained his decisive 3-pointer from along the right sideline.
The Gophers' guard sealed the victory with a steal and a pair of free throws, finishing with 17 points and five rebounds for Minnesota (17-5, 5-4 Big Ten), which won a second straight following a four-game skid.
Andre Hollins provided 15 points, eight assists and six boards in the victory.
Mike Gesell led the Hawkeyes (14-8, 3-6) with 11 points and six rebounds while Zach McCabe and Aaron White each added 10 points in the loss.