Echefu was a perfect 11-for-11 from the free-throw line, and Mims made 9-of-11. Echefu added seven rebounds, and an emphatic block with time winding down.
Florida State (12-4) trailed by nine with 7:14 left in the game, but the Seminoles scored seven straight to pull within two. With the game tied at 69, Jason Rich made a layup to give the Seminoles their first lead since halftime.
The Explorers (4-8) were led by Rodney Green's 16 points. Jerrell Williams added 12 points and 14 rebounds, and Darnell Harris scored 13. LaSalle shot 50-percent from the field, and outrebounded the Seminoles 34-25.
Florida State scored 25 points on LaSalle's 16 turnovers, including a Toney Douglas steal and layup with 1:41 left in the game that gave the Seminoles a 73-69 lead.
Jason Rich scored 16 points for the Seminoles. Toney Douglas added 12, and Isaiah Swann scored 11.