Rivers said a lot of that has to do with the Clippers playing better defense.
"I think it helps when you rebound better," Rivers said. "It usually means you're getting stops, No. 1. That to me is what rebounding is. You have a rebounding opportunity. If you're getting a lot of stops, there'll be a lot of rebounds."
The Clippers were out-rebounded in their first six games, but out-rebounded their opponents in the last two games before they played Chicago on Monday night.
Even with that, the Clippers were grabbing 37.1 rebounds per game as a team, the second-lowest total in the league.
Clippers center DeAndre Jordan has been doing his job on the backboards. He was leading the NBA in rebounds before Monday night's game, averaging 11.9 per game.
Though Jordan is getting more than his share of rebounds, Rivers said it's important for everyone on his team to crash the boards.
"DJ is going to get rebounds, so we don't have to ever worry about him," Rivers said. "But the stops come from everyone, and the more we keep guys out of the paint, the more effective we are and the better rebounding team we are.
"But, DJ has been amazing. He's been good."
Clippers reserve guard Jordan Farmar still is trying to find his way this season.
Farmar was signed over the summer to a two-year deal to replace the departed Darren Collison, who signed with Sacramento.
But Farmar entered Monday night's game averaging just 13.9 minutes per game and just 3.8 points on 32.3% shooting,
Rivers said Farmar's play has been "up and down" so far this season.
Rivers said some of it is because Farmar is still learning the Clippers' system and learning how to "run the offense better."
"But more for Jordan, my whole focus for him is being a better defender," Rivers said. "I know it's in there, and I know he can be that. I would say I'm probably the hardest on him about that than anything else."
Chris Douglas-Roberts, who has a strained right Achilles' that is expected to keep him out for about two weeks, said he first felt the injury during the summer, but didn't think it was that serious.
Douglas-Roberts said Monday night that he thought he just had "some soreness in my Achilles'."
But he kept playing through the summer, training camp and the early part of the season.
But he got an MRI that revealed a serious injury.
"The big thing is just getting healthy for the first time in a long time," Douglas-Roberts said. "That's what I'm looking forward to."