The Wolverines moved into the finals of the Puerto Rico Tip-Off by rallying from a 16-point deficit early in the second half. Michigan will meet Charlotte in the championship game Sunday.
Stauskas hit his key layup with 8 seconds to go in regulation and scored six of his 26 points in overtime. Two foul shots by Derrick Walton with 14 seconds to go in the extra period gave Michigan a 5-point cushion.
The Wolverines improved to 4-1 and handed the Seminoles their first loss in five games.
Walton added 15 points and Mitch McGary came off the bench to score 14 points and grab 12 rebounds.
Florida State was led by Okaro White with 18 points and 12 rebounds.