Florida held the Bulldogs scoreless for the first 5:30 while building an 11-0 lead. Georgia did not get to 10 points until 4:20 remained in the first half.
Rosario finished with 19 points, and both Patric Young and Erik Murphy had 11 for the Gators (11-2), who shot 53 percent from the field and went 12-of-26 from 3-point range.
It was the Southeastern Conference opener for both teams.
Kentavious Caldwell-Pope was the only player in double figures for Georgia with 11 points. The Bulldogs fell to 6-8.