Marcel White made five 3-pointers for Jacksonville (11-11, 3-2 Atlantic Sun) and scored 17 points.
The Dolphins combined to shoot 13 of 27 from beyond the arc.
Leading by nine at halftime, Jacksonville increased its lead to 16 on a layup from Babineaux with 10:27 remaining. Upstate closed the gap to six on a 3-point play from Josh Cuthbertson with 1:21 left, but the Spartans missed their next six shots from the floor.
Cuthbertson's layup with five seconds left gave him 17 points in the half and a career high-tying 20 overall for Upstate (7-15, 1-4). Michael Buchanan scored 24 points on 11-of-16 shooting and grabbed a career-best 13 rebounds.