Minutes before Miami's two quick touchdowns, the Hurricanes (5-3, 2-2 Atlantic Coast Conference) appeared to have lost their best chance to get the win when Kirby Freeman was stopped for no gain on a fourth-and-1 at the Florida State 1 with 5:29 left and the 'Canes trailing 29-24.
Lee threw two interceptions and lost two fumbles for Florida State (4-3, 1-3). He completed 14 of 32 passes for 208 yards in his third start this season.
The Seminoles wasted five field goals by Gary Cismesia and Antone Smith's first 100-yard game of the season. Smith finished with 114 yards on 22 carries.
Cismesia's fourth field goal, from 45 yards, gave Florida State a 26-24 lead late in the third quarter of the back-and-forth contest and he added another from the same distance early in the fourth quarter for the 29-24 lead.
The Hurricanes had grabbed a 24-23 lead on a trick play midway through the third quarter when place-kicker Francesco Zampogna took an over-the-shoulder toss from his holder and found tight end DajLeon Farr on a 26-yard scoring pass.
Wright, who hurt his left ankle, was 6 of 10 for 88 yards, but threw an interception that put Florida State into a 17-14 lead.
Toddrick Verdell's 45-yard touchdown run was followed by a Cismesia field goal that put the Seminoles ahead 20-17 at halftime.
Miami also scored two quick touchdowns in the first quarter to grab an early 14-3 lead.
The Hurricanes went ahead 7-3 lead on Wright's 1-yard run on a scoring drive highlighted by Wright's 64-yard third down pass to Darnell Jenkins.
Greg Cooper then added a 2-yard TD run set up by a fumble by Florida State's Smith.
Florida State coach Bobby Bowden, who has 370 career coaching wins, is now just one ahead of Penn State's Joe Paterno.