"Without C.P., we know we have to take care of home games," said Jared Dudley, who scored 18 points.
Darren Collison had 15 points, six assists and five rebounds in place of Paul, who is out six weeks with a separated shoulder. DeAndre Jordan had 11 points and 13 rebounds in giving Clippers coach Doc Rivers a second victory against his old team this season.
"The first quarter, we were really good, then we played in spurts," Rivers said. "We had a chance early to throw a knockdown and we didn't. They almost pulled it out."
Los Angeles improved to 12-10 without Paul in the lineup since he arrived in 2011.
"Nobody can make up for that, so we have to lean on each other," Crawford said about Paul's loss.
Jordan Crawford and Avery Bradley scored 24 points each in Boston's sixth consecutive loss overall and ninth in 10 games. The Celtics have dropped six in a row on the road while continuing to struggle without injured Rajon Rondo, who has a torn ACL in his right knee.
Jared Sullinger was called for a flagrant-1 technical on Griffin with 10 minutes left in the game. Griffin was driving to the basket when Sullinger ended up on Griffin's back.
"I told Blake, 'My bad if you thought I was a little rough,' and he said he understood," Sullinger said. "He's just protecting himself, just like I was protecting myself. So there really wasn't any chippiness between me and Blake. We were just playing physical basketball."
It was Sullinger's fifth flagrant this season and third in two nights. He received two in Boston's 129-98 loss at Denver on Tuesday, although one of those was rescinded earlier Wednesday.
"I've just got to adjust. I thought I adjusted a little bit today," Sullinger said about his latest. "I tried to back him up, then I put my hands up to try to show him that I wasn't trying to do anything. But I guess I've got to make another adjustment."
Boston trailed 88-82 to start the fourth, but quickly fell behind 100-84. Griffin hit 3 of 5 free throws, and Willie Green and Crawford made 3-pointers that helped stretch the Clippers' lead. Griffin played nearly all of the second half.
"That's not the minutes I want to play Blake, but you can get away with it every now and then," Rivers said.
After Sullinger's flagrant, Boston outscored the Clippers 21-11 to end the game. Trailing 109-105, Jerryd Bayless missed a shot with 8 seconds to go, ending the Celtics' late push.
"At that point, they're playing with nothing to gain and we're playing with everything to gain," Celtics rookie coach Brad Stevens said. "It's a lot easier to play when you're behind in that moment than when you're ahead. I thought we were very aggressive, we had a quick lineup on the court, and it helped that Collison fouled out with 57 seconds or so left. That actually made me feel like we had a shot because there was one less ballhandler for them."
Ahead 74-72 in the third, Griffin made a monster dunk over Kris Humphries, who fouled the Clippers' big man.
"I don't know if you saw me, but I was like, 'Oh my god, that was nasty!' " Jordan said. "I was trying to hurry up and see the replay."
Jamal Crawford added: "I can't wait to go home and watch it on YouTube."
Boston took its first lead since the opening quarter, 72-71, with less than 5 minutes left in the third on Humphries' first basket. That capped a 13-4 spurt in which the Celtics rallied from eight points down. He started in his return from a sprained left ankle that kept him out of the loss to Denver.
Dudley hit three consecutive 3-pointers as the Clippers led 53-42 in the second. Boston had a 13-6 spurt, including six by Bradley, to get within one. Jamal Crawford made three straight free throws to keep the Clippers ahead 59-55 at halftime.
The Clippers used an 18-0 run with five different players scoring in the first quarter to take their largest lead of the game, 26-10.
Clippers G J.J. Redick could return Friday against the Lakers. He has been out with a broken right hand and torn ligament in his wrist. G Reggie Bullock will miss the next game with a sprained left ankle. ... Rivers said the Clippers would work out veteran F Hedo Turkoglu, who has been without a team since he was released by Orlando last fall. ... The Celtics fell to 2-8 in the second game of a back-to-back this season.