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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.