The Hurricanes used an 8-0 run late to close the gap to 64-62 with 46.4 seconds left, but Terance Manns putback with 29 seconds remaining gave the Seminoles breathing room. Mann finished with nine points and seven rebounds.
Phil Cofer added seven points and six rebounds for the Seminoles (12-2, 1-1 ACC).
Chris Lykes scored 17 points and Anthony Lawrence II added 14 for Miami (8-6, 0-3). Ebuka Izundu had 13 points and nine rebounds.
Florida State adjusted its rotation frequently on a night when it was called for 20 fouls, including 12 in the first half. The foul trouble neutralized a significant depth advantage over Miamis eight-man rotation.
Florida State shot 42 percent (27 of 64) from the floor and made 23 percent (6 of 26) of its 3-pointers.
Miami shot 38 percent (20 of 53) from the field and hit just 22 percent (4 of 18) of its 3s.
Dejan Vasilijevic was averaging 44 percent from 3-point range but was held to just a pair of 3s in 29 minutes.
Miami: The Hurricanes have dropped their last three games at Florida State and are 8-31 overall in Tallahassee.
Florida State: The Seminoles have won five straight against teams from the Sunshine State, a streak that includes wins over Florida in November and North Florida in December.
Miami hosts Wake Forest on Saturday.
Florida State hosts No. 1 Duke on Saturday.