The margin stayed between seven and 11 points, and Memphis still lead by 10 approaching the 4-minute mark.
The Clippers scored six straight to cut it to 92-88 with 2:47 left. Matt Barnes connected on a 3 from the right corner to bring Los Angeles within 94-91 with 2:12 remaining. A little over a minute later, a pair of free throws from Paul brought the Clippers within 98-96 with 1:05 left.
That was as close as Los Angeles could get as Memphis scored the last four points for the win.
As has become the norm when the two teams face each other, the play was physical and defense stout.
That lead to the Clippers going to the line 23 times in the first half, but Los Angeles converted only 13 of them.
Meanwhile, Memphis was 2 of 3 in first-half free throws.
But Memphis connected on 50 percent of its shot to carry a 53-50 lead into the break. Johnson came off the bench for 13 points, including a dunk in traffic, after throwing the ball off the backboard to himself.
The Clippers used 15 first-quarter points from Griffin to open an early lead. He would end up with 16 for Los Angeles, while Crawford had 12 at the half.
Memphis maintained its lead through the third, and led 73-68 as they started the rally that would create a 12-point lead in the fourth, its largest of the night.
NOTES: Griffin has scored at least 25 points in 10 straight games. . The Clippers and Grizzlies have played 23 times since Jan. 26, 2012, including 13 games in the postseason. . The loss snapped the Clippers three-game regular season winning streak in Memphis. . The Grizzlies promotion Friday night was a temporary "GRIZZLIES" neck tattoo as a nod to reserve F James Johnson, who has his son's name NAYMIN tattooed around his neck. . Memphis G Tony Allen returned after missing 21 games with a sprained left wrist. The Grizzlies were 16-5 during his absence. He scored 9 points, converting all four of his shots.