Jesse Morgan had 12 and Williams finished with 10 for UMass (9-3), which has won six straight games. The Minutemen also secured their seventh straight road victory, the program's longest road streak since the 1997-98 season.
UMass led 37-29 at intermission but watched Miami (5-7) open the second half on a 9-2 run, cutting the deficit to 39-38. From there, the teams battled through eight lead changes and five ties until Williams' jumper gave UMass the lead for good, 70-69, with 1:12 left.
Allen Roberts led Miami with 21 points.
Pirates catcher Jacob Stallings, the son of University of Pittsburgh basketball coach Kevin Stallings, made his major league debut on Sunday night.
Who made the biggest impact at the NBPA Top 100 camp? We update several top prospects such as Zion Williamson.
The only thing that can sink John Calipari's star-studded ship is a leadership void, but Isaiah Briscoe seems to have that covered.