Darian Townes had 11 points and six rebounds for the Razorbacks (2-0), who advanced to a second-round game against Providence, which beat Temple, 66-64, in a first-round game Thursday.
Sonny Weems scored 10 points and pulled down six rebounds for Arkansas.
Dustin Scott scored 12 for the Cougars (0-2), who will play Temple Friday in the consolation game.
Arkansas took matters in hand early, scoring the first 11 points of the game and holding the Cougars scoreless for the first 8:30 of the game.
College of Charleston scrapped back to within 26-24, but then the Razorbacks finished the first half with a 7-1 run. Arkansas opened the second half with a 13-4 run to take control for good.
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