The Hurricanes rode big performances by Jarrett Payton and Jon Peattie and a key play by D.J. Williams.
Miami (11-2) defeated the Seminoles (10-3) for the fifth straight time, benefiting from a crucial missed field goal for the fifth time in the series since 1991.
Xavier Beitia, who was wide left on a potential game-winning 43-yard field goal in last year's loss at Miami, was wide right on a 39-yarder with 5 1/2 minutes to go.
Florida State's defense held, but in punt formation on fourth and one from its 31, Miami snapped the ball to Williams, who rumbled 31 yards for a key first down that helped take two more minutes off the clock.