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.