USF took control quickly with a 14-3 first quarter advantage, but Syracuse pulled within 21-13 by halftime.
USF held Syracuse to no first downs and scoreless in the second half.
Grothe completed 19-of-26 passes for 248 yards and ran for a score after a team-high 72 yards on 10 carries.
Syracuse running back Curtis Brinkley gained 112 yards on 20 carries with one touchdown.
Quarterback Cameron Dantley completed 11-of-27 passes for 129 yards, while placekicker Patrick Shadle booted two field goals for the Orange (1-6, 0-3), who have dropped three in a row.