Hibbert also grabbed 10 rebounds while Paul George added 22 points and 10 assists for the Pacers, who needed key foul shots from George and Tyler Hansbrough down the stretch to pull out the win.
David West supplied 16 points, seven rebounds and six assists for Indiana, which blew 24-point lead before eventually edging the Clippers.
Lance Stephenson and George Hill each netted 13 points in the win.
Los Angeles got 25 points from Jamal Crawford in the loss, including 15 in the fourth quarter.
Blake Griffin added 17 for the Clippers.