De'Cody Fagg had four catches for 95 yards, highlighted by a 70-yard touchdown catch for Florida State (3-1).
Alabama starter Drew Weatherford was pulled in the second quarter after completing 7-of-11 passes for 42 yards. John Parker Wilson completed 28-of-53 passes for 240 yards and two touchdowns for Alabama (3-2).
D.J. Hall had seven catches for 83 yards and a touchdown for the Crimson Tide.
The game was scoreless at halftime. The Seminoles got moving with Lee on their first drive of the second half -- an eight-play, 67-yard scoring march to give Florida State a 7-0 lead with 10:50 left in the third quarter.
A Wilson turnover early in the fourth quarter set up an Antone Smith tally and gave the Seminoles a 14-0 lead with 9:03 remaining. Alabama out-scored Florida State, 14-7, in the final five minutes.