Maxie Esho's dunk with 1:01 remaining put the Minutemen in front for good and Massachusetts held the Hawks scoreless over the final 2 minutes.
It was the opening Atlantic 10 Conference game for both teams, and Saint Joseph's appeared on its way to an upset win when Halil Kanacevic scored on a layup to give the Hawks a 57-48 lead with 6:23 remaining.
A 3-pointer by Williams was among the key shots during the surge that finished the contest.
Williams scored 22 points in helping boost Massachusetts to 13-1 for the season. Esho had 12 points and Raphiael Putney added 11.
All but nine of Saint Joseph's points came from Kanacevic, who had 19, Langston Galloway, who contributed 18, and DeAndre Bembry, who had 16. The Hawks fell to 9-5.