Trailing 36-25 early in the second half, New Orleans (3-4) used a 17-3 run that included a pair of 3-pointers from Gill to close the gap and later took the lead for good on a three-point play from Gill that made it 51-48 with 2:22 left.
Jordan Caroline hit a jumper at the other end to bring Southern Illinois (7-5) within a point but Nate Fry responded with a 3-pointer and Gill closed out the game with a pair free throws.
Tevin Broyles also had 11 points for the Privateers, who shot 47.5 percent from the floor and were 14 of 14 from the free throw line.
Anthony Beane led Southern Illinois with 12 points and Caroline scored 10 and grabbed five rebounds.
