Andre Hollins chipped in 13 points for Minnesota (24-13), which advances to Thursday's title game against SMU.
Okaro White tallied 16 points and 12 rebounds, Ian Miller added 16 points and Devon Bookert netted 13 points for Florida State (22-14).
The Golden Gophers led by as many as 15 points in the first half, when they shot 38.5 percent from the floor, including 7-of-14 from 3-point range. The Seminoles shot at a 36.8 percent clip, but went 1-of-9 from beyond the arc. Minnesota led 30-20 at intermission.
Minnesota led for most of the second half until White sank a pair of free- throws with 4:10 left in regulation to give the Seminoles a 51-50 edge. The Golden Gophers responded with an 8-2 run to take a 58-53 lead with 26 seconds to play. However, the Seminoles weren't done yet, as Bookert scored seven points in the final 21 seconds, including a 3-pointer with less than a second to play to force overtime.
In the extra session Maurice Walker hit 6-of-8 free-throws to help Minnesota pull away from the Seminoles, who went 1-of-8 from the field and 2-of-4 at the charity stripe in the period.