Vinson scored 20 points on 6-of-12 shooting, including four from deep, while Riley tallied 18 points, all from 3-point range. Trey Davis came off the bench to score 12 for UMass (18-9, 8-6 Atlantic 10 Conference), which shot a season-high 52 percent (13 of 25) from beyond the arc.
UMass took a 69-62 lead on Vinson's trey with 6:23 remaining.
Xavier's Travis Taylor followed an Isaiah Philmore 3-pointer with a free throw to cut the deficit to 69-66, but the Musketeers (16-12, 8-6) made just 2 of 7 shots and committed two turnovers over the final 5 minutes as UMass slowly pulled away.
The Minutemen converted 49 percent (27 of 55) from the field to overcome a 41-30 rebounding deficit.
Semaj Christon led Xavier with 17 points and Philmore added 14.