LeBron James led the Cavaliers with 29 points and Brown had 20 to go along with eight assists.
Cleveland won its second in a row and moved within five games of Orlando for the third spot in the Eastern Conference.
The Cavaliers saw a late seven-point lead cut to two thanks to the long-range shooting of Richardson, but Brown's two free throws fought off the Charlotte comeback. Cleveland won the season series 3-1.
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