Rudy Gay added 14 points for Memphis.
Mo Williams had 20 points for the Clippers while Chris Paul scored 19 and Blake Griffin had 15 points and 11 rebounds. Paul and Griffin both missed time in the fourth quarter with injuries.
Paul strained a groin muscle and appeared to jam a finger while Griffin hyperextended his left knee.
Paul almost singlehandedly gave the Clippers a chance to close out this series by scoring eight of his 27 points in overtime of Game 4.
This time, the four-time All-Star guard had just five points by halftime and scored nothing in this fourth quarter.
He was grimacing early in the fourth quarter and was on the bench with the injured right groin. An injured groin kept him out of the Clippers' regular season finale, a loss to New York that cost Los Angeles the No. 4 seed.
The Clippers came in needing a win to clinch their first series since 2006 and advance to a second-round series against top-seeded San Antonio.
But even though Paul has plenty of postseason experience, this was the first close-out game for the likes of Griffin, Randy Foye and DeAndre Jordan.
Los Angeles last led at 17-16 before a fastbreak layup by Tony Allen that was set up by a long pass from Gasol put Memphis ahead to stay at 18-17 with 5:40 left in the first quarter.
The Clippers closed the third quarter with a 14-2 run and got within six twice to conjure up memories of Memphis blowing a 27-point lead in Game 1.
Foye pulled the Clippers within 85-79 on a layup with 55.7 seconds left.
With CP3 on the bench, that was as close as they would get.