Blake Griffin had 30 points and seven assists before fouling out with 2:26 left in overtime for the Clippers, who blew a 10-point lead in the final 4½ minutes of regulation before their All-Star point guard took charge in the overtime.
Mike Conley scored a career playoff-high 25 points and Rudy Gay had 23 on 8-of-25 shooting for the Grizzlies, who couldn't match Paul's late-game poise in another thrilling chapter of a highly entertaining series.
Game 5 is Wednesday night in Memphis, with Game 6 back at Staples Center on Friday if necessary.
After Paul hit consecutive jumpers in the final 1:16, Conley's layup with 8.1 seconds left trimmed the Clippers' lead back to two points. But Mo Williams added two free throws with 7.2 seconds left, and Gay missed a meaningless 3-pointer at the buzzer.
Griffin and Paul embraced while another frenzied sellout crowd of long-suffering Clippers fans roared.
Caron Butler, playing with a broken bone in his left hand, scored 14 points for the Clippers, who still shouldn't be comfortable in a thrilling series with Memphis, which outrebounded Los Angeles 47-36, but couldn't close the victory.
In their breakthrough season since pairing Paul with Griffin, the Clippers need one more victory to win their second playoff series since the erstwhile Buffalo Braves moved to California. Los Angeles beat Denver in the first round in 2006, but hadn't been back to the postseason until this spring.
After the Clippers rallied from big fourth-quarter deficits in their first two victories, Memphis trimmed a late 84-74 deficit to 85-83 on Zach Randolph's jumper with 1:25 left. Gay hit the tying jumper in the final minute of regulation, and Paul drove for the go-ahead layup — his only points of the fourth quarter — before Randolph coolly hit two tying free throws with 20.4 seconds left.
Paul couldn't get a shot on the final possession of regulation, with Tony Allen and Gay swarming him.
The Clippers led 95-89 when Griffin fouled out, and the Grizzlies trimmed it to two points on jumpers by Conley and Gay. Paul went to work, shaking loose from defenders and hitting back-to-back jumpers sandwiching a turnover by Conley.
Fans filled Staples Center well before tipoff, donning their giveaway red T-shirts and standing to cheer on the majority of Los Angeles' possessions. They raised Staples Center's intensity to a level it hadn't seen since ... well, Sunday, when the Los Angeles Kings' fans roared throughout their second-round NHL clincher over St. Louis.
The tone was set in the first quarter: In a scintillating 2½-minute stretch, the teams combined for six 3-pointers, an alley-oop from Paul to DeAndre Jordan and a technical foul for Gay. Butler, who broke his hand in the opener and sat out Game 2 before surprisingly returning for Game 3, scored 11 points and checked out to a standing ovation in the first quarter.
Memphis kept constant pressure on Griffin, forcing the two-time All-Star to be resourceful while keeping his temper in check. Randolph got a technical foul in the second quarter when he fouled Griffin roughly on the shoulder and then chest-bumped him, but Griffin only chuckled while Randolph, the former Clippers big man, was pulled away from him.
The Grizzlies got tough, but the NBA's leaders in steals didn't get a single steal in the first half.
Notes: The NBA finalized the start time for Game 5 in Memphis. It will begin at 9:30 p.m. EDT. ... Paul went flying over the front row of seats to chase a loose ball with 45.8 seconds left, gingerly making his way back to the bench. ... After going 13 for 30 on free throws in Game 3, the Clippers made 10 straight to open Game 4, but finished 28 of 40. ... Fans near courtside included Clippers stalwarts Billy Crystal and Penny Marshall. Former Clippers guard Sam Cassell, now an assistant coach with the Wizards, watched the game with Washington guard John Wall.
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