The Clippers won 107-101 on Monday night after blowing much of a 15-point lead and went 3-1 playing four games in five nights to start the season.
Paul notched the NBA's first triple-double of the season and his first with the Clippers, finishing with 13 points, 12 assists and 10 rebounds. He showed no ill effects after spraining his left foot a night earlier.
"We won, so that's all that matters," said Paul, who got 2 1/2 hours of treatment on his foot to be able to play.
Paul was the leading rebounder for the Clippers, who got outboarded 51-37.
"When he's going after rebounds like that, I guess it's hard for our bigs to crash," Utah's Gordon Hayward said. "A lot of those rebounds were defensive, so when our bigs are crashing, that can be a load down there."
Crawford had missed Sunday's loss to Sacramento because of bruised ribs and said he still feels only 70 percent. He returned to go over the milestone on a floating jumper at 6:53 of the fourth and has totaled 15,003 points in his 14-year career.
"It's a pretty good number," Crawford said. "I've been really consistent."
"The kid is amazing," Clippers coach Doc Rivers said of Hayward. "I've had a man crush for two years."
There were eight lead changes, but the Jazz never led by more than two points. Their last lead came on Rudy Gobert's dunk early in the fourth. They got within one twice more, but the Clippers found ways to keep extending the lead.
"There were a lot of breakdowns, and that can't happen against a team like that," new Jazz coach Quin Snyder said. "They know what they're doing and they're really connected, so it's tough to withstand that. You expend a lot of energy coming back, and they made plays down the stretch."
After struggling offensively in their first three games, the Clippers got untracked by shooting 51 percent and making 15 of 17 free throws.
The Jazz ran off 13 straight points to tie the game at 62 in the third. Hayward hit a 3-pointer and added a steal and layup in the spurt. Griffin and Paul combined to score eight straight before Bullock's fourth 3-pointer kept the Clippers ahead 73-70 going into the fourth.
It was Paul's 12th career triple-double and the first for the Clippers since April 3, when Griffin had 25 points, 10 rebounds and 11 assists against Dallas. "He did a great job coming in and stealing some of our rebounds," Griffin said.
Retired Hall of Fame coach Jerry Sloan is attending Jazz practices under Snyder. "We try not to bug him, but he's there to support us and help me personally and our whole staff," Snyder said, adding that he wants to maintain the tradition within the franchise.
Jazz: F Joe Ingles of Australia, who got cut at the end of the preseason by the Clippers, had no points in 10 minutes.
Clippers: F Glen Davis is likely to return Wednesday after missing the first four games with a strained right groin.
Jazz: Host LeBron James and the Cavaliers on Wednesday.
Clippers: Visit Golden State on Wednesday.
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