The band, which was backed by Darryl Jones on bass, Chuck Leavell on keys, Bobby Keys on sax and Bernard Fowler and Lisa Fischer as backup singers, encored with the hits "Brown Sugar" and "Jumpin' Jack Flash."
"(This is) the first show of the tour, probably the best one," Jagger said at the end of the 90-minute set.
Bruce Willis, Gwen Stefani and Skrillex were among the famous faces in the sold-out crowd.
Rumors of the surprise show spread across social networks last week after the band teased the appearance on their Twitter accounts. The dance-pop band New Build, which was originally scheduled to play the Echoplex on Saturday, was first to leak details about the performance.
"Our gig got shifted b/c the Rolling Stones are playing Echoplex," the band posted Friday on Twitter. They joked that they were looking forward to "having it out" with the Stones.
The Rolling Stones performed a few dates together in London, Brooklyn, N.Y., and Newark, N.J., last winter, but didn't announce a tour until earlier this month. They will play 17 dates in the United States but said they may add more down the line. The lowest price for tickets to the show at the Staples Center, which has a capacity of about 20,000, is $250.
Follow AP Entertainment Writer Derrik J. Lang on Twitter at http://www.twitter.com/derrikjlang