The game was slowed by the referees, who called Memphis for 29 fouls and the Clippers 28.
Memphis owned a 48-46 edge in scoring in the paint, while the Clippers dominated 25-5 in second-chance points.
Griffin and Randolph staged a wrestling match within the game. Griffin said his back, which had spasms in the regular-season finale on Wednesday, felt good.
"I'm ready for however many games it's going to take," Griffin said. "If that's the way he wants to play, let's do it."
Randolph said: "It's not that big of a deal right now. We want to win the next one. If we can't win the next one, then it's a big deal."
The Grizzlies never led, and it didn't help that Randolph picked up two fouls and Mike Conley Jr. had three in the first half. Besides Griffin, Jordan had four fouls, while Matt Barnes, Lamar Odom and Ronny Turiaf had three apiece for the Clippers.
"They had two or three guys going to the glass every time," Conley said. "They were jumping over us and using their athleticism."
Paul scored his team's first seven points in the third, extending the lead to 64-53.
The Clippers led 57-51 at halftime after Barnes tipped in Paul's miss just before the buzzer. They led by 13 points early in the second before the Grizzlies cut it to two points twice in the final 1:24.
NOTES: The Clippers have won eight straight games, including their final seven of the regular season. ... Los Angeles is in the playoffs for the second straight year, the first time that's happened since 1991-92 and 1992-93. ... Memphis led the NBA in points allowed with 89.5 per game in the regular season.