Ryan Anderson missed a shot for the Hornets that would have forced overtime, leaving the Clippers with their fourth straight victory.
Los Angeles overcame a six-point deficit to start the fourth quarter and Paul hit six free throws over the final 17 seconds to help the Clippers pull out the win.
Blake Griffin led the Clippers with 20 points and Paul had 17 to go with 14 assists.
Eric Gordon scored 25 for the Hornets, who lost their third in a row.
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