Griffin had 22 points and 14 rebounds, Butler scored 20 points against the team he suffered a season-ending injury against last January, and the Clippers beat the severely undermanned Milwaukee Bucks 92-86 on Saturday night.
"I love it," said Billups, who scored 19 points. "I love it because your stars don't have to be superstars every night. They can lean on other guys when it's not going so well."
The chippy game resulted in a combined 54 fouls, including a flagrant 1 against Milwaukee's Larry Sanders for his hard takedown of Butler on an attempted layup with 1:38 left in the third quarter.
Paul finished with nine points and seven assists.
"We have so many scorers and so many weapons that even if the ball doesn't go in sometimes, we'll still be able to score points," Griffin said. "As good as our new guys are, that's what makes that transition easier. Guys like Chauncey and Caron, because of how good they are and how hard they work and how much they love the game, it just flows a little bit better than it would otherwise."
The last time Butler played against the Bucks, on New Year's Day 2011 with Dallas, he ruptured a tendon in his right knee while going for an offensive rebound at Milwaukee. He underwent surgery and missed the rest of the Mavericks' championship season, then signed with the Clippers as a free agent.
"He's highly motivated, coming off that injury, and he's going to have a great year," Billups said. "I don't know if people forgot, but Caron has been one of the best small forwards in the game in the last seven, eight, nine years. He probably flew under the radar because he didn't play much last year. But we know about him, and he won't be a secret for long."
Brandon Jennings scored 21 points and had seven assists for the Bucks, who have lost four straight. They played their third in a row without center Andrew Bogut, who is in Australia attending to personal matters with his family. Teammate Luc Richard Mbah a Moute, who helped UCLA reach the Final Four in 2008, missed his third in a row because of tendinitis in his right knee.
In addition, swingman Mike Dunleavy Jr. was sidelined by a groin problem, reserve guard Beno Udrih also sat out with an injured left shoulder, and reserve forward Jon Brockman left the game for good midway through the second quarter because of a bruised left eye.
Drew Gooden again started in Bogut's place, contributing 18 points and 13 rebounds in 29 minutes. The Bucks are off to their first 0-5 start on the road since 2004-05, when they dropped their first seven.
"We need somebody to step up and knock down shots for us," said forward Stephen Jackson, who was 4 for 18. "It has been difficult on this trip, for sure. We haven't gotten anybody with any consistency knocking down shots. We're not playing a very efficient game right now."
Paul took a breather after getting his fourth foul with 2:17 left in the third quarter and Los Angeles leading 65-59. He was replaced by Randy Foye, who had played only six minutes to that point despite his 14-point fourth quarter in Wednesday's 117-89 win over Houston.
The Clippers still had a four-point lead when Paul reported back in with 9:55 remaining, and they stayed in front the rest of the way. Paul hit a 20-footer with 2:23 remaining to help clinch it.
"I never go into a game saying I'm going to get 15 or 20 points. I'm just going to take whatever the defense gives me," Paul said. "Tonight Chauncey got it going -- and Blake, obviously. That's how it's going to be with this team all season long. You've got to win games like this. When it's all said and done, it's not about the stats. It's about the won and lost columns."
Milwaukee led 40-38 at halftime despite shooting 35 percent. The Clippers took charge in the third quarter with a 14-2 run that gave them their biggest lead, 63-50, with 4:48 left in the period.
"Defensively, we just have so much room for improvement," Griffin said. "We played poorly on defense tonight, and luckily they missed some shots."
The 3-point shooting was poor at both ends of the court. The Clippers missed their first nine attempts -- all in the first half -- and finished 4 for 19. The Bucks were 6 for 20 after missing 10 of their first 12 from behind the arc.
Forward Reggie Evans grabbed six rebounds in his Clippers debut after being sidelined for the first five games of the season because of a sprained right foot. The ninth-year veteran averaged a career-high 11.5 rebounds in 30 games with Toronto last season.
The Bucks shrugged off a seven-point deficit and took their first lead 38 seconds into the second quarter on a layup by Jennings that put them ahead 19-17. Clippers reserve guard Ryan Gomes picked up three fouls in his first 7 minutes on the floor and was back on the bench with 10:18 left in the half.
This was the teams' only meeting this season due to the reconfigured 66-game schedule caused by the lockout. ... Paul extended his streak to 15 consecutive games with at least one steal when he stripped the ball from Gooden with 4:16 left in the second quarter. ... The Clippers had 14 turnovers against a Bucks defense that had forced an average of 19.2 over their first six games.