Langford, a freshman guard, had 22 points and seven rebounds.
Justin Smith had 12 points and six rebounds, and Rob Phinisee and Alijami Durham scored 11 points each for the Hoosiers (14-14, 5-12 Big Ten), who ended a five-game skid.
Ethan Happ had 23 points and 11 rebounds, Khalil Iverson had 15 points, and D’Mitrik Trice scored 12 for the Badgers (19-9, 11-6), who had won their five previous games against Indiana and came into Bloomington as 2½-point favorites.
Langford’s basket came after Trice made three free throws to tie the game at 73 with 9 seconds remaining in the second overtime period.
Trice had forced the first overtime with two free throws to tie it at 62 with 5 seconds left in regulation. He later tied it at 68 with a 3-pointer, leading to another overtime.
Langford gave Indiana the boost it needed, scoring nine points after regulation.
The Hoosiers built a 10-point lead with an 8-2 run at the start of the second half. An alley-oop from Phinisee to Smith put Indiana ahead 41-31 with 16:32 left in regulation.
Davis’ free throw midway through the second half to make it 47-34, the Hoosiers’ biggest lead.
Then Wisconsin went on a big 20-3 run to regain the lead. Happ scored the go-ahead basket before Trice’s 3-pointer gave the Badgers a 54-50 edge with 6:52 left in regulation.
Indiana took a lead with a late first-half surge, scoring six straight at the start of an 11-2 run. Langford made back-to-back baskets, including a 3-pointer with 5:59 left in the half to put the Hoosiers ahead 23-19. Indiana led 33-29 at halftime.
Wisconsin: With three regular-season games remaining before the start of the Big Ten Tournament, the Badgers still have a chance to get on a roll going into the postseason with two of the next three games at home.
Indiana: The Hoosiers stuck around in losses last week to ranked opponents Purdue and Iowa. Indiana finally got over the hump with three games left before the conference tournament.
Wisconsin hosts Penn State on Saturday.
Indiana hosts No. 6 Michigan State on Saturday.
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By JIM JOHNSON , Associated Press