Willie Green added 11 points and 11 rebounds for his second-career double-double for the Hatters (5-10, 2-2).
Perez hit 9 of 14 and Pegg 10 of 19 as Stetson shot 50 percent (31 of 62) from the field. Joel Naburgs had eight of the team's 24 assists.
Perez snapped a 32-all tie with a layup with 3:50 left until halftime, and Stetson closed the half on a 10-2 run. Glenn Powell hit a layup for Jacksonville 42 seconds into the second half, but then Stetson scored seven straight for a 49-36 lead.
Jacksonville got within six, 78-72 with 18 seconds left, but no closer.
The NBA draft is Thursday night (7 ET, ESPN/WatchESPN), and trade talk is picking up. Chad Ford dishes his latest intel on how the draft will go and which teams will make deals.
Get to know the NBA's next crop of superstars.
Marc Spears speaks with Chris Washburn, who was drafted third overall in the 1986 NBA Draft, about how drug addiction cost him almost everything, including his life.