The Gators (10-3) scored 13 of the game's first 14 points and led the Blue Hose (2-12) by more than 30 for most of the second half.
Parsons' all-around game as Florida's sixth man included two 3-pointers and three dunks.
Tyus' 16 points and 13 rebounds marked his first double-double since the season opener. Murphy, who had been battling a shoulder injury, set career highs with 16 points and 11 boards off the bench.
The Gators outrebounded the Blue Hose 51-29 and had a 46-12 edge in points in the paint.
Jake Troyli led Presbyterian with 14 points.
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