Patric Young (14 points, seven boards) and Erik Murphy (12, seven) also played big roles as the Gators (12-2, 2-0 SEC) recorded their fourth straight win.
Boynton's two 3-pointers sparked a 21-5 run after halftime that allowed Florida to grab control of the contest.
LSU (9-4, 0-2) was led by Anthony Hickey with 15 points.
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