Chris Paul scored 29 points and Los Angeles forced a Game Seven in their first-round series against Utah.
The Clippers beat the Jazz 98-93 and will host the only do-or-die game of the first round on Monday, with the winner advancing to face the Golden State Warriors.
Los Angeles began to edge away in the third quarter and appeared to be in control when Austin Rivers capped a 9-2 run with a step-back three-pointer that pushed the lead to 91-77 with 3:58 remaining.
He hit another with 1:29 left to make it 96-86, but Gordon Hayward scored seven straight to bring the Jazz within three before Joe Johnson missed a three-pointer in the waning seconds which would have tied the game.
DeAndre Jordan had 13 points and 18 rebounds for the Clippers, while Hayward ended with 31 points for the Jazz.