Earlier in the day, NBA Commissioner Adam Silver handed out a life ban to Sterling and fined him $2.5 million for racist comments that stunned the league and the nation.
It was a strong statement warmly applauded by the NBA as a whole, and the Clippers in particular.
While questions remain concerning Sterling's future ownership of the team, and the impact of his comments on the players, the NBA's stern decision has unquestionably lightened the Clippers load.
"I am drained," Rivers told reporters before the start of Game Five against the Golden State Warriors in their best-of-seven play-off series.
"But not drained enough not to go out and coach this game.
"I thought that was the sigh of relief we needed," Rivers said, referring to Silver's announcement earlier in the day. "Is this over? No, it's not over. But it's the start of a healing process that we need.
"We're going to let this whole thing run its course and then we'll all have better clarity. I want my players to be comfortable, honestly. I think that's the most important thing."
Silver, who has urged the NBA's owners to vote to force Sterling to sell the Clippers, has received universal backing throughout the league for his handling of the incident.
"My team-mates and I are in agreement with his decision," said Clippers guard Chris Paul, who is also the NBA's Players Association president.
"We appreciate the strong leadership from Commissioner Silver and he has our full support."
Fans at the Clippers' home Staples Center venue appeared to share Paul's sentiment, and the earlier ruling took the steam out of what was expected to be an unsettled environment.
There was a surprisingly low-key atmosphere outside the arena a few hours before Tuesday's game with just a smattering of protesters and Clippers fans wandering around with placards held high.
"We Are One. LA Clippers" read one banner, echoing the three words posted on the Clippers website earlier in the day in a clear response to the Sterling controversy which had engulfed the team since the weekend.
Another placard bore the words: "Silver Shines Bright. Thank You", while two others read: "End Racism" and "No Bigots Allowed".
Police security was more visible than usual outside the arena for a Clippers game.
An LAPD officer told Reuters: "It's been more low-key here today than it was yesterday when people were wondering what sort of response would be made by the NBA on the Sterling matter.
"Silver's announcement today has taken a lot of the tension out of the air."
The Clippers locker room was closed to the media prior to Game Five, which has the best-of-seven-series tied 2-2.
The team went through their standard pre-game warm-up and the vocal fan contingent made a point to show their support.
"I do think (the Staples Center) will be a safe haven and our crowd will be amazing," Rivers said. "I do think that will help."
The distraction did the Clippers no favours on Sunday for the team's first game following news of Sterling's controversial comments when they were blasted in a 118-97 Game Four defeat at Golden State.
The Clippers had considered boycotting that game in defiance of their owner.
"They did talk about it. I thought the black socks and the shirts (the Clippers wore in protest) was fine," Rivers said.
"My father, who is no longer here, would've told me to go do my job and don't let anyone stop you from doing your job."
With the NBA, the commissioner, and their home fans behind them, the Clippers are back in position to do just that.
- Sports & Recreation