Rodney Williams scored 14 points and Julian Welch added 10 for the Golden Gophers (13-5, 1-4 Big Ten), who had lost four straight. Minnesota shot 6 of 13 on 3-pointers in the first half to take the lead, then maintained it by scoring in the paint and grabbing 12 offensive rebounds in the second half.
Indiana freshman Cody Zeller matched a season high with 23 points for the Hoosiers (15-2, 3-2). Jordan Hulls scored 13, Will Sheehey 12 and Victor Oladipo 10 for Indiana, which had won three straight.
The Hoosiers were 11-0 at home, including victories over then-No. 1 Kentucky and then-No. 2 Ohio State.
Minnesota had been close in three of its four Big Ten losses. The Gophers lost in overtime at Illinois, by five at Michigan and by two at home against Iowa.
Minnesota seemingly had Thursday's game under control with a six-point lead and the ball in the final minute. But Zeller stole the inbounds pass, and a three-point play by Oladipo cut Minnesota's lead to 71-68 with 40 seconds to play.
Minnesota's Joe Coleman calmly sank two free throws with 39 seconds remaining before Sheehey drained a 3-pointer at the other end to cut Minnesota's lead to 73-71 with 30 seconds left.
Coleman was fouled with 28.6 seconds left, and again, he made both foul shots.
Zeller scored and was fouled with 17.3 seconds left. His free throw cut Minnesota's lead to 75-74.
Minnesota's Austin Hollins made a pair of free throws with 15.1 seconds left. Watford missed a 3-pointer and Minnesota rebounded. Welch missed a pair of free throws with 2 seconds left to give the Hoosiers one last shot. Watford's pass was intercepted by Maverick Ahanmisi at halfcourt, and time expired.
Minnesota led 37-34 at halftime, then scored the first six points of the second half to make Indiana's fans restless. A jumper and a putback by Sheehey brought the crowd back into the game, but Minnesota, which softened up Indiana's defense with the 3-point shot in the first half, resorted to attacking the rim in the second. A layup by Williams increased Minnesota's lead to 51-40.
Indiana went on a 7-2 run to cut Minnesota's lead to 53-47. The Gophers led 68-62, and Indiana's crowd was back into the game before Minnesota worked the clock, then Sampson drained a baseline jumper to push the lead to eight points with 1:43 to play, setting up the wild finish.