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.
Leaving early for the NBA is a risky decision. Some players -- Skal Labissiere, Dejounte Murray -- slid in the draft. Some -- Isaiah Taylor, Troy Williams -- weren't drafted at all.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?
The Tar Heels could lose Justin Jackson and Kennedy Meeks after next season. Coach Roy Williams has nearly every top-10 2017 prospect on his board.