Licata completed 18 of 30 passes for 226 yards in only his third start of the season.
Buffalo (4-7, 3-4) trailed 13-0 at halftime but Kyn Minniefield returned a punt 35 yards for a touchdown to cut the deficit to 13-7 in the third quarter.
After Michael Cox’s 3-yard touchdown expanded UMass’ lead to 19-7, Licata capped off back-to-back Buffalo drives with touchdowns to give the Bulls their first lead of the day, 22-19.
Brandon Murie added a 12-yard touchdown run late in the fourth quarter to put the game away.
Murie finished with 90 yards on 16 carries.
Mike Wegzyn led UMass (1-10, 1-6) with 215 yards through the air but threw two second-half interceptions.