Hill, a freshman averaging 10 points a game, badly sprained his left ankle early in the second half and had to be helped to the locker room. He did not return.
The injury could be problematic for Florida (3-1), which already is without point guard Scottie Wilbekin. The senior is suspended indefinitely, but he could return as early as next week.
The Gators had little trouble without Hill against the Jaguars (1-4).
Casey Prather had 10 points and nine rebounds, one of three players in double figures, as the Gators extended their home winning streak to 18. Florida led by 16 at halftime and cruised from there.
Calvin Godfrey led Southern with 18 points and nine rebounds. Trelun Banks added 12 points.
Florida dropped five spots in the latest AP Top 25 poll, a result of losing at Wisconsin last week.
The Gators responded with a lopsided win against Arkansas Little-Rock on Saturday, a game in which they scored 59 points in the second half. Coach Billy Donovan's team carried that momentum into Monday night's game despite having just two days' rests.
Hill had a layup, a reverse layup, and a runner in the lane that helped Florida build a double-digit lead early. Prather kept getting in the lane and to the free-throw line, and Florida eventually pushed the advantage to 16 points before the break.
They coasted from there, far from good enough to appease Donovan. The coach called several timeout in the second half and even got caught screaming at Michael Frazier II in an emptying arena.
Frazier scored nine points, hitting 3 of 7 shots from 3-point range.
Patric Young finished with a season-high 12 points and six rebounds. DeVon Walker had 10 points, and Dorian Finney-Smith chipped in eight points and seven rebounds before fouling out.