Charles had six points and Scott Plaisance, Troy Green and Rosser five each in a 25-1 over a 5 1/2-minute stretch to put New Orleans comfortably ahead 86-49.
Charles was 8-of-10 shooting with three 3-pointers and a game-high seven rebounds while Rosser was also 8 of 10. Plaisance added 14 points and Amari Haynes 13.
The Privateers (3-2) shot 58 percent and made 18 steals, in scoring 31 points off 27 turnovers. They outscored the Jaguars 48-16 in the second half after leading 49-37 at the break.
Justin Siorek scored 21 points with five 3-pointers and Robbie Brooks added 10 points for Governors State.
The Jaguars, who began playing varsity basketball in 2015-16 and reached the NAIA Tournament last season, were playing a NCAA Division I opponent in a regular-season game for the first time.