Harper finished the game 14-for-24 with 160 yards and James Davis rushed 18 times for 102 yards and a TD for the Tigers (1-0), who have won four of the last five games they've played against the Seminoles.
Clemson jumped to a 21-0 lead when Harper hit Aaron Kelly for a 41-yard TD early in the second quarter and led 24-3 at halftime before withstanding an FSU comeback attempt in the second half.
It marked the ninth time FSU's Bobby Bowden and his son Tommy, the head coach at Clemson, have faced off against each other. The elder Bowden holds a 5-4 edge but has lost three in a row now.
2014: The Year in Music [PHOTOS]