Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood were joined by their original bass player Bill Wyman at the O2 Arena as the ageing rockers performed their first major concert for five years.
Lead singer Jagger made light of criticism of the ticket prices for the sold-out gig - fans had paid up to £406 ($AUD623) for a standard seat, and thousands of pounds more on ticket re-selling sites.
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"How're you doing in the cheap seats? They're not that cheap though, that's the problem," Jagger joked as the concert began.
The band opened with "I Want to be Your Man", with 69-year-old Jagger strutting around the giant stage dressed in a silver jacket and trilby, before launching into "Get Off of My Cloud".
US soul diva Mary J Blige joined Jagger to sing the female lines of "Gimme Shelter" and legendary rock guitarist Jeff Beck added a flourish to "I'm Going Down".
The Stones welcomed on stage another former member, guitarist Mick Taylor, to play on "Midnight Gambler".
Jagger donned a black feathered cape to perform "Sympathy For The Devil" while a demonic red light was trained on him, before a rousing rendition of "Jumping Jack Flash" ended the night.
The Daily Telegraph's music critic Neil McCormick said the Stones rose to the occasion, laying claim to the title of the world's greatest band "with some style and panache".
Noting that one of the encores was "You Can't Always Get What You Want", McCormick wrote: "Well, maybe sometimes, for the right ticket price, you actually can."
Tickets for Sunday's gig and the second London concert on Thursday were snapped up in seven minutes last month.
But the Telegraph said that just hours before the show began scores of tickets remained unsold on re-selling websites after standard tickets were inflated to £1,300 ($AUD1993).
The London shows are the first part of the "50 And Counting" performances to mark the Stones' half century in the music business, with a concert in New York and two in Newark, New Jersey to follow next month.
Diehard fans said they had broken the bank to snap up tickets because it might be the last chance to the see their heroes in action.
Jill Roberts, a 52-year-old housewife from England, said as she entered the O2: "It's hard to justify that kind of money but a lot of people were prepared to pay it.
"It's an awful lot of money but I guess it's just a one-time thing. I don't think I'll be coming again anyway."
She first saw the Stones play eight years ago. "I want to experience it again, because they are such good musicians," she said.
The band have been rehearsing in Paris, where they played a concert for just 350 people at a small club on October 26, although tickets for that surprise gig were priced at just 15 euros ($AUD 24.70).
US music magazine Billboard reported in August that the Stones would earn a total of $25 million ($AUD 23.9 million) for the four shows - and that was before the extra date in New York's Barclays Center on December 8 was added to the itinerary.
