Gasol also contributed 13 rebounds and Randolph had nine boards as Memphis won its second straight to ensure another stop in Tennessee for Game 6. Mike Conley had 15 points and 13 assists, and Tayshaun Prince scored 15 in his best game of the series.
"Now we got to go out there and try to get a win," Memphis coach Lionel Hollins said.
Paul and Blake Griffin had 19 points apiece for the Clippers, and Griffin also grabbed 10 rebounds for his first double-double this postseason. Los Angeles' reserves outscored its counterparts again, 43-16. But DeAndre Jordan was the only other starter besides Paul and Griffin to score for the Clippers, and he had two points. Chauncey Billups and Caron Butler went a combined 0 for 10 from the floor in being shut out.
Game 5 is Tuesday night in Los Angeles.
"We got to go back, and we got to take care of business in Game 5 at home in front of our fans," Clippers coach Vinny Del Negro said. "But there's no question we're going to have to get back to playing the way we did the first couple games."
The team that controls the boards has won each game of the series so far, with Memphis owning a 45-28 advantage in Game 4. That led to a 22-2 difference in second-chance points, boosted by a 13-5 edge on offensive boards.
The Grizzlies used their prowess on the glass to beat the speedy Clippers when it came to fast-break points, 18-6.
Memphis' biggest advantage is its big men, and Randolph and Gasol each took turns helping the Grizzlies turn this into a best-of-three series. Gasol had six points at halftime, and Tony Allen said Hollins chewed out the 7-foot-1 Spaniard at the break, reminding him to score.
"The second half, he was just phenomenal," Allen said.
P Tuesday, 8:30 p.m.
Series tied 2-2