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.