Webb rushed for 189 yards on 20 carries and threw for 221 yards as the Blazers (1-0, 1-0 Conference USA) accumulated 513 yards of total offense.
UAB took a 27-3 halftime lead behind Webb, who accounted for the game's first four touchdowns. He had scoring runs of 15 and 71 yards and completed touchdown passes of 9 and 22 yards to Frantrell Forrest as UAB took a 27-3 halftime lead.
Forrest finished with four catches for 64 yards and Jeffrey Anderson had three receptions for 65 yards.
Nick Fanuzzi rushed for an 8-yard score and completed a 52-yard touchdown pass to Luke Willson for Rice (0-1, 0-1).
Fanuzzi was 12 of 20 for 154 yards.