Webb was 14-for-19 passing for 292 yards for the Blazers (4-5), while the quarterback also ran for 120 yards on 15 carries. He scored on runs of 36, 22, 24 and 17 yards. He also had rushing scores of 65 and 2 yards.
Rashaud Slaughter rushed for 104 yards on four carries, including a 31-yard rushing score to give UAB a 35-14 lead in the first half.
The Owls (3-5) cut the lead to 35-21 just before halftime on Jeff Van Camp's 22-yard touchdown pass to Jamari Grant. But Florida Atlantic would get no closer as the Blazers answered with three straight touchdowns in the third quarter.
Van Camp was 24-for-36 passing for 254 yards, three touchdowns and two interceptions for the Owls.