The reigning NBA champion Dallas Mavericks were fighting for their playoff lives, facing elimination in game four of their Western Conference first-round series.
Chris Paul scored 24 points and handed out 11 assists for the Clippers, who took a 2-1 lead in the best-of-seven series, with game four on Monday in Los Angeles.
Rudy Gay finished with 24 points for Memphis, but missed a potential game-winning jump shot at the buzzer.
The Grizzlies led 71-64 going into the fourth quarter. The visitors were up 79-73 when the Clippers' Eric Bledsoe made a layup to launch a 13-3 scoring run by Los Angeles.
Foye's three-pointer tied the score at 80-80. Paul then made a jump shot, stole the ball from Gasol to feed Griffin for a dunk and made a pair of free-throws as the Clippers seized an 86-80 lead with 23 seconds to play.
The Grizzlies kept chipping away, and had a chance to pull out the win until the bitter end.
Western top seeds San Antonio were in action later, seeking to take a 3-0 lead over Utah.
Source: AFP American Edition