Rayvonte Rice scored 13 points for the ninth-seeded Illini (19-13), who will advance to take on top-seeded Michigan in the quarterfinal round Friday.
Yogi Ferrell scored 14 points and Will Sheehey added 13 points for the eighth-seeded Hoosiers (17-15), who stayed close with the Illini but couldn't get over the hump in the second half.
Down 38-33 early in the second half, the Illini went on a 15-2 run to take the lead. Jon Ekey's three-pointer with 8:42 left capped the surge and gave Illinois a 47-40 cushion.
Indiana remained within striking distance but could never take the lead.
Austin Etherington hit a layup with 3:13 left to draw the Hoosiers within 53-52, but after the Illini came up empty on the other end, Noah Vonleh attempted a jumper that would have given Indiana the lead, but was blocked by Nnanna Egwu.
Tracy Abrams responded with a three-pointer for Illinois with 2:06 left to extend the lead to two possessions, 56-52. He then hit a pair of free throws with 1:19 left to make it a six-point game, 58-52.
Illinois hit four more free throws down the stretch before Indiana got its next bucket to ice the win.
Kendrick Nunn ended with 10 points for Illinois, which outscored Indiana 11-2 to end the game.
Illinois jumped out to a 9-0, but Indiana responded with a 14-2 run, capped by a Ferrell three-pointer with 10:38 left. Play remained close the rest of the half, with Illinois carrying a 30-28 lead into the break.
Troy Williams had 11 points for Indiana.