Terrell threw two touchdown passes in the second quarter - both to Daniel Braverman for 31 and 57 yards - and Franklin's 39-yard TD run gave the Broncos a comfortable 35-19 lead at the break.
Franklin led the Broncos (1-1) with 210 yards on 33 carries, surpassing his 163-yard effort against Purdue to start his freshman season.
The Vandals closed within 12 points after Matt Linehan threw a TD pass to Justin Podrabsky with 3:22 left in the third, but Franklin answered with a 7-yard touchdown run to end the quarter. Linehan's 75-yard TD pass to Joshua McCain with 2:38 left in the fourth closed the deficit to 12 once more.
Linehan threw for three touchdowns and ran for another to lead the Vandals (0-2).