Western Carolina held a 48-47 lead before Wiggins knocked down a trey and Baru converted a layup to put Charleston ahead 52-48 with 3:05 left.
The Catamounts cut the deficit to 52-51 but Lawrence scored four straight points to give the Cougars a 56-51 lead with only 54 seconds left.
Charleston made six free throws in the final minute to seal the win.
The Cougars shot just 27.1 percent (16 of 59) from the field but played tough defensively, recording 10 blocks and five steals.
Brandon Boggs led Western Carolina (10-16, 4-9) with 15.