The game-winning shot as time expired gave the fourth-seeded Clippers as 2-0 lead in their first-round Western Conference playoff series against the Grizzlies.
Paul's clincher came after the Grizzlies had rallied from 12 points down late in the game, forging a 91-91 tie on Marc Gasol's slam dunk with 13 seconds left.
Paul netted the Clippers' final eight points, finishing with 24, nine assists and four rebounds, while Blake Griffin added 21 points, eight boards and four helpers in the win.
Jamal Crawford came off the bench to put in 15 for Los Angeles.
Mike Conley led the fifth-seeded Grizzlies with 28 points and nine assists.
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