The Titans (2-0), who hadn't played since defeating Division III Redlands 118-68 on Nov. 11, led 35-29 at halftime in the Beryl Shipley Classic at the Cajundome.
The Colonels (0-3) got to 63-60 with 4:51 to play, but scored only three points the rest of the way.
Both teams shot about the same from the field -- with Cal State Fullerton at 46.7 percent (21 of 45) and Nicholls State at 46.9 percent (23 of 49) -- but the difference came at the free-throw line.
The Titans hit 24 of 35 foul shots while the Colonels were just 12 of 21.
Chris Talkington led Nicholls State with 17 points.