The Gators held the Lions without a point during the opening 6:57 of the second period while expanding their lead to 24 points.
Rosario added six points and four assists while hitting 8-of-13 from the field.
Michael Frazier II added 12 points for the Gators and Patric Young had 10. Florida (8-1) bounced back from its first loss of the season, which came last Saturday against Arizona.
Southeastern Louisiana (1-8) lost its fifth in a row. The Lions were paced by Brandon Fortenberry with 15 points.