Memphis, down by two with five seconds to go, was forced to miss a final free throw and the ploy worked in that the Tigers' Wesley Witherspoon ended up with the ball. But his shot was blocked by Williams and Arizona's Jamelle Horne grabbed the loose ball.
The victory sends the Wildcats (28-7) into a third-round pairing Sunday against West Region No. 4 seed Texas (28-7), which defeated Oakland 85-81 earlier Friday. Memphis was sent home with a 25-10 record.
The score tied at 68 when Tarik Black completed a 3-point play for Memphis. Lamont Jones snapped that tie with a 3-point shot with 1:37 to play and a pair of Jordin Mayes free throws had the Wildcats ahead 73-68 with 54 seconds to go.
The difference was still five when Memphis's Joe Jackson made two free throws with 20 seconds left and, after a turnover, Jackson had a layup that cut the lead to one. But Jones made two more free throws and Arizona, ahead 77-74, fouled Jackson, setting up the intentional miss.
Williams had a team-high 22 points and 10 rebounds and Jones scored 18 points for Arizona. Memphis was led by a 17-point effort from Antonio Barton.