Northwestern's Tre Demps, who made his first start this season as part of a juggled Wildcats lineup, finished with 19 points. Alex Olah added 17 and 11 rebounds.
The Hoosier's run started with a 6-2 spurt to close out the first half. Indiana lead 32-30 after 20 minutes after Vonleh hit a layup as time ran out.
The Hoosiers opened up their widest advantage, at 12 points, 7:25 into the second when Stanford Robinson hit a pair of free throws to make it 44-32. Northwestern shot just 1 for 8 from the floor to open the half and connected at 38.8 percent for the game.
Demps closed it to 54-50 with 2:21 left when his layup was counted on a goaltending call, but Williams replied with a layup on the next Indiana possession.
Indiana avenged a 54-47 loss to Northwestern at Bloomington, Ind. on Jan. 18. The Hoosiers hadn't won since a 63-53 upset of Michigan on Feb. 2.
Northwestern's losing streak dates to a 55-54 win at Minnesota on Feb. 1.
Northwestern coach Chris Collins was forced to shuffle his lineup as his second-leading scorer, JerShon Cobb, missed the game with a foot injury.
That allowed Demps, who entered the game as the Wildcats third leading scorer, to make his first start this season. He had come off the bench in all of Northwestern's 27 previous contests, averaging 10.9 points per game.
Guard Dave Sobolewski, who had averaged fewer than 2 minutes in Northwestern's last six, also started.
The Hoosiers lost 82-64 at Purdue last in their last game last Sunday. They were done in by a 19-1 Purdue run midway through the game in that one.
Indiana's last scheduled game, versus Iowa at Bloomington, Ind. on Tuesday, was postponed several hours before tipoff after an 8-foot piece of metal fell from the ceiling at Assembly Hall. The game will be made up on Thursday.
Neither Indiana nor Northwestern was able to open more than a four-point lead in the first half, or take control in a back-and-forth opening period marked by missed open shots, and bouts of scrappy play and loose ball control.
Olah led all scorers in the first with 12 points. Northwestern's beefy 7-foot center was 5-for-8 from the floor, and a couple of times looked surprised that he had an open shot. Demps added nine points, including two 3-pointers.
Both teams came out cold, each missing on its first four shots from the floor. Indiana's Sheehey dropped in a layup 3:52 in for first field goal of the night.
Northwestern moved ahead 9-8 on Drew Crawford's 3-pointer at 6:36 the Wildcats held the advantage until Gordon's 3 later made it 17-16.
Indiana flashed a little flair late in the first with four straight dunks, three by Williams, to start its late run. The Hoosiers then took charge early in the second.
Sheehey's 3-pointer with 52 seconds left made it 59-51 and iced it.