Paul tried to carry the Clippers by himself because his running mate, Blake Griffin, could only play 19 minutes 34 seconds because of a sprained right ankle.
But for as much as Paul did in tying his career playoff high with 35 points, he alone couldn't take down the Memphis Grizzlies, who won Game 5, 103-93, Tuesday night at Staples Center.
Game 6 is Friday night in Memphis, where the Clippers lost Games 3 and 4 by an average of 16.5 points. Now they must win there if they want to force a Game 7 here Sunday.
"We've got to be desperate," said Paul, who was 11-for-24 from the field. "That's how it is. You say the playoffs don't start until somebody loses at home. I guess ours started."
And here is something else for the Clippers to ponder: The team that has won Game 5 of a series that was tied at 2-2 has advanced to the next round of the playoffs 84% of the time.
"We've got to stay the course and go there with the right mind-set," Clippers Coach Vinny Del Negro said. "We have to put ourselves in position like they did tonight and get a win."
When Paul entered the interview room after the game, he had his left hand wrapped with ice on it, looking like it was injured.
"I'm cool," Paul said about his hand. "I hit myself."
The Clippers fell behind by 13 points in the third and trailed by eight at the end of the quarter.
But when Gasol picked up his fifth foul with 10:23 left, the Clippers looked as if they might get back into the game.
Matt Barnes made both free throws after the foul to pull the Clippers to within four points.
But Randolph, a 6-foot-9, 260-pound power forward, scored 10 of his 25 points in the fourth quarter, Tayshaun Prince (15 points) made a big-time three-pointer with 1:29 left and Gasol scored down low for a 96-88 Memphis lead. That spelled the end for the Clippers with 48.8 seconds left.
Randolph finished with 11 rebounds, and Gasol, the Grizzlies' mountainous 7-1, 265-pound center, had 21 points and eight rebounds. Mike Conley also helped out Memphis' cause, scoring 20 points and handing out six assists.
Griffin suffered a sprained right ankle at practice Monday, but still started Tuesday.
He had four points, five rebounds and five assists, but with 5:39 left in the third quarter he limped off the court and into the locker room for the second time in the game. This time, he didn't return.
Griffin was hurt during the team's walk-through at practice Monday. He went up for a dunk and fell over backup forward Lamar Odom just as the team was about to finish practice.
Griffin first went to the locker room after the first quarter and returned to the court with 8:50 left in the second quarter.
"I give Blake a lot of credit," Del Negro said. "He's got a lot swelling in there. But he got therapy all night and all day. He battled through it. But as the game went on, it just got obviously fatigued and sore and worse and worse. You could see in the third he was struggling to move a little bit. That's when I pulled the plug on that."
Griffin's problems weren't limited to his ankle; he also picked up two fouls in the second quarter, giving him three in the first half.
The Clippers were called for three three-second defensive violations in the second quarter, technical fouls that resulted in three easy points for the Grizzlies — one of several factors that helped put the Clippers in a 54-48 halftime hole.
They never caught up, trailing the entire second half.