The Minutemen (19-4, 6-3 Atlantic 10) shot 53.1 percent from the field and outrebounded Rhode Island 36-27. Raphiael Putney chipped in 11 points.
The Rams had moved out to a 62-55 lead with 8:35 remaining as Munford had a layup and three free throws. UMass responded, surging back into the lead after a Williams jumper and going up 68-65 after a Gordon layup.
After a block by Putney on T.J. Buchanan, Williams made two free throws. Matthews hit a 3-pointer to pull Rhode Island within two with 15 seconds left, but Trey Davis followed by sinking three free throws, capping an 18-6 UMass run to ice the game.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.