Paul's no-look, bounce pass to Blake Griffin for a slam-dunk with 1:23 remaining in the fourth quarter capped an 11-1 run that saw the Clippers grab control after trailing by as many as eight points in the second half.
But Los Angeles had to hold off a game-ending Memphis surge and barely hung on to post a 2-1 lead in their Western Conference quarterfinal series when Rudy Gay missed potential score-winning 3-pointer at the buzzer.
Griffin finished with 17 points and Randy Foye sank four 3-pointers en route to 16 for Los Angeles.
Gay netted 24 points and Zach Randolph added 17 for the Grizzlies, who will attempt to even the series in Monday's Game 4 at Staples Center.
Swim Week Miami Beach 2014 [PHOTOS]