Chris Hetland also kicked three second-half field goals for the victors.
Chris Leak was 17-of-26 for 179 yards for the Gators (3-0, 1-0), who have started the season with three straight wins and won their SEC home opener for the 14th time in the past 15 seasons.
Florida Coach Urban Meyer ran his overall winning streak to 19 straight games, which includes 16 in a row with Utah. Meyer has the second longest active winning streak in the country behind only Southern California's Pete Carroll.
Erik Ainge was 14-of-29 for 147 yards with a touchdown while Gerald Riggs Jr. rushed for 86 yards for the Volunteers (1-1, 0-1).
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