The 49ers (2-0), who led by three after a back-and-forth first half, held the Eagles scoreless for the first 5:46 of the second half, and built a 50-36 lead with 11:57 remaining.
Charlotte dominated Georgia Southern on the boards 40-19, including 21-8 in the second half.
Braswell, who had 16 points in the first half, and teammate DeMario Mayfield both missed the season opener for violating team rules, but Mayfield's suspension was for two games.
Pierria Henry added 13 points for the 49ers while JT Thompson, a transfer from Virginia Tech who missed the opener because of an injury, played 15 minutes and chipped in four points.
Eric Ferguson and Cleon Roberts led the Eagles (0-2) with 11 points each, and Ferguson also had 10 rebounds.
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