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.
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point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.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.