Dawson finished with 7-of-14 shooting from the field for the Flames (4-13, 1-3 Big South). Caleb Homesley added 12 points with five rebounds and Lovell Cabbil had 11 points, six rebounds, four assists and five steals.
Dawson's game-winning 3-pointer came with 13 seconds to play and Liberty trailing 61-59. An earlier 3-pointer by Dawson gave the Flames a 53-52 lead with 3:05 to play but they fell behind by two on a layup by Coastal Carolina's Elijah Wilson with 40 seconds to go.
The Flames trailed by as many as 10 early in the second half.
Wilson led the Chanticleers (8-7, 2-3) with 15 points and eight rebounds.