The Tigers (8-3, 6-2 ACC) won their sixth consecutive game, but had the Atlantic Division wrapped up as they kicked off thanks to North Carolina's 31-13 victory against Boston College.
Clemson will face Coastal division winner Georgia Tech in two weeks at Tampa, Fla.
Spiller had a 4-yard touchdown run and set the ACC's single-season all-purpose yardage mark, surpassing the 2,059 of Virginia's Thomas Jones in 1999.
Virginia (3-8, 2-5) kept things close in the first half, its 21 points more than it had put up in any of its previous five games. However, the Cavaliers were shut out the final 30 minutes and lost their fifth in a row.