Chris Paul had 24 points and 11 assists and high-flying Blake Griffin added 17 points for the Clippers, who beat the Memphis Grizzles 87-86 on Saturday only after Gay missed a 3-pointer just before the buzzer.
"That's the way we planned it," Paul joked. "They aren't going to give us anything. They're never out of the game with an electrifying scorer like Rudy Gay."
The Clippers won their first home playoff game in six seasons to take a 2-1 series lead in the Western Conference playoffs. Game 4 is Monday night.
The long-suffering Clippers fans, who turned Staples Center into a sea of red, very easily could have gone home disappointed.
Paul hit a fadeaway jumper with 2:02 left for an 82-80 lead. On the next possession he had a no-look bounce pass to Griffin coming in off the baseline for a monster slam.
Trailing 86-80 after two free throws by Paul, Gay hit a 3-pointer with 12.9 seconds left, Memphis' first field goal since 7:10. After Los Angeles missed three of four free throws, Gay hit another 3-pointer with 8.9 seconds to hush the crowd.
Eric Bledsoe missed two more free throws, Gilbert Arenas rebounded for Memphis to set up Gay's final shot. Gay, who had 24 points, got some room to shoot, and quickly let go. But it the shot bounced off the rim.
"At the end of the game, I wanted to make a quick play," Gay said.
Memphis had another big advantage at the free throw line, like it did in winning Game 2, but couldn't capitalize. The Grizzlies made 30 of 39 while the Clippers were just 13 of 30.
"We missed 17 free throws?" Paul said. "We did? It shows how much fight we have. It's unacceptable."
Paul did his part at the line, making, seven of eight. But Griffin missed six of nine while Reggie Evans missed six of eight.
Memphis had seemingly taken the crowd out of the game in the third quarter, when it outscored the Clippers 25-14 to take a 71-64 lead.
The Clippers' lull extended into the fourth quarter. Marc Gasol made a field goal with 7:10 left for a 77-71 lead, but that was Memphis' last basket until the first of Gay's two 3-pointers in the closing seconds.
"We shut down and only scored 15 points in the fourth quarter," Memphis coach Lionel Hollins said. "We took too many quick shots and gave up second-chance points. We gave them the back door and Blake took advantage of it."
Said Gay: "We missed a couple plays we wish we had back. We had a couple letdowns."
The Clippers, who rallied from 27 down to win the opener on Sunday night at Memphis, started this comeback with just more than four minutes to go.
Evans made a strong inside move against Marreese Speights to rebound Bledsoe's missed free throw and score to pull L.A. to 79-77 with 4:08 left. Randy Foye then hit a huge 3-point shot from the left side with 3:13 left to tie it at 80 before Paul and Griffin took over.
"He's tenacious," Gay said of Paul. "He doesn't give up. He makes plays and finds people. We can't have other people doing what they did today. The Clippers pushed us tonight. They got into the lane. We'll see how we respond on Monday."
Forward Caron Butler started for the Clippers, wearing a splint on his broken left, or non-shooting, hand. He was hurt in Game 1, and missed the next game. He scored four points.
The Clippers used an 18-1 run spanning the first and second quarter to take a 36-23 lead, but the Grizzles turned around and dropped a 13-0 run on Los Angeles to tie it.
Griffin put an exclamation point on the first half when he stole the inbounds pass from Speights and swooped in for a dunk at the buzzer to give the Clippers a 50-46 lead.
It was the first home playoff game as Clippers for Paul and Griffin.
"I won't forget my first playoff in this building," Paul said. "The energy in the crowd and seeing fans celebrating motivate us. The crowd won the game for us."
Said Griffin: "It was unbelievable. The fans were on their feet and with the energy through our warm-ups, we had no choice but to play hard."
Foye had 16 for L.A.
Clippers coach Vinny Del Negro tried to play coy before the game about Butler's status, but added after: "Maybe we underestimated how tough he is" ... Paul was impressed that Butler played. "If he can fight with one broken hand, what can the rest of us do?" ... Butler played just more than 22 minutes. ... Gay committed two fouls in the game's first five minutes and sat out until early in the second quarter.