Paul scored 13 of his total in the fourth quarter and the extra frame for the Clippers, who won for the sixth time in seven games.
Blake Griffin notched 18 points and 10 rebounds as Los Angeles went 22-of-25 from the foul line to secure the victory.
The Clippers also got 18 points from Chauncey Billups before he left midway through the fourth quarter with a twisted left ankle.
The Magic, meanwhile, saw their three-game winning streak snapped despite 33 points and 14 rebounds from Dwight Howard.
Jameer Nelson re-entered the lineup after missing five games with a concussion and contributed 15 points with 12 assists.