With Los Angeles leading by just two points in the last minute, Paul twice pushed the Clippers' edge back to four with a jumper and two free throws and finished with his team's final five points to seal the road victory.
It was the seventh successive win for the Clippers (15-6), their longest stretch since taking eighth straight in the 1991-92 campaign.
Paul finished with 18 points while Blake Griffin added 22 and 10 rebounds in the triumph.
Carlos Boozer led the way with 24 points and 13 rebounds for the Bulls, who fought back from a nine-point deficit in the fourth quarter to make the Clippers sweat.
Chicago (11-9), still playing without Derrick Rose as well as Richard Hamilton, had a three-game win streak snapped. (Writing by Jahmal Corner in Los Angeles;Editing by Peter Rutherford; )