Dawson hit four 3-pointers on the night, and finished 5 of 9 from the field. Caleb Homesley finished with 15 points and Evan Maxwell had 10 for the Flames (9-15, 6-5 Big South), who have won four straight games.
DeSean Murray scored 23 points to lead Presbyterian (8-13, 3-7). Reggie Dillard and Ed Drew each had 9 points.
Liberty led 37-32 at the break and never trailed in the second half. A Murray layup cut the Flames lead to 56-54 with 4:46 to play. But Maxwell hit two free throws, Homesley nailed a 3, and Dawson added another at the line to push the lead back to 62-55.
Presbyterian managed to get to within three twice more, but Dawson finished 3 of 4 at the line to seal the win.