The Hoosiers tied the game at 52-52 with five minutes, 46 seconds left when junior guard Mark Johnson, an Oregon, Wis., native, knocked down his fourth 3-pointer of the game.
Williams, though, took over down the stretch, scoring 10 points, including two consecutive 3-pointers, in an 11-2 run over the next three minutes. He finished with 20 points and seven assists.
"Knowing Deron for so long, I have seen his development as a basketball player, especially on the offensive side," said Indiana guard Bracey Wright, who played with Williams in high school. "He has become a fun player to watch on the court. In high school, he was not a very good shooter and did not look for his shot. You can see that he has spent a lot (of) time on his shot because he is very confident every time he shoots the ball, and he's ready to take the big shot when he is needed."
Head, who had a career-high 29, hit 6 of 6 free throws in the final 2:11 to help ice it.
Johnson led Indiana with a career-high 16 points, one day after scoring a then career-high 13 in a first-round win over Ohio State.
Freshman guard Dion Harris hit six 3-pointers and paced fifth-seeded Michigan with 23 points in a quarterfinal win over Iowa Friday afternoon.
Wing Lester Abram added 19 points and fellow sophomore Daniel Horton contributed 14 for the Wolverines, while senior wing Bernard Robinson, Jr. nearly had a triple-double with nine points, eight rebounds and a tournament-high 10 assists.
The Hawkeyes trailed by as many as 21 points in the second half but fought back and closed the gap to 67-63 with less than three minutes to play. Abram, though, scored seven points in the final 2:37 to help Michigan pull out the win.
Iowa sophomore guard Pierre Pierce led all scorers with 28 points.
The Wolverines next play No. 1 seed Illinois, Saturday at 12:40 p.m. CST.