The Rolling Stones' hit-packed Glastonbury debut has been hailed as "the high spot of 43 years" of the festival by organiser Michael Eavis.
The band opened with Jumpin' Jack Flash, with Mick Jagger prowling the stage in a green sequinned jacket.
He repeatedly thanked the crowd and, after It's Only Rock 'N' Roll (But I Like It), joked organisers had "finally got round to asking us" to play.
Tens of thousands of fans cheered on the two-hour set featuring 20 songs.
Speaking immediately after the band came off stage, festival boss Eavis called it "the high spot of 43 years of Glastonbury".
"They finally did it, and it was fantastic. My God, did they deliver."
Eavis also said he had bumped into Prince Harry at the festival during the day, "and I recommended he stay the night".
The Stones had arrived on stage after an intro tape featuring the sounds of Worthy Farm's usual residents, 350 dairy cows.
Eavis was heard saying "we waited a long time" as the unmistakable rhythm track of Sympathy For The Devil played and the crowd spontaneously broke into the familiar "whoo whoo" backing vocals.
"It's great to be here doing this show, doing this festival," said Jagger after It's Only Rock 'N' Roll (But I Like It).
"After all these years they finally got round to asking us," he added. Drummer Charlie Watts gave the joke a desultory cymbal crash.
The band had modified the Pyramid stage with three catwalks, allowing Jagger to bridge the cavernous gap that separates most Glastonbury performers from the audience.
It was in almost constant use as the 69-year-old strutted back and forth, clapping his hands thrusting his thick-lipped pout into the air.
Five songs into the set, Jagger introduced a new song, written for a girl "in cut-off jeans" he claimed to have met at the festival on Friday night.
A swampy country-rock number, it featured the refrain "Waiting for my Glastonbury girl".
Keith Richards, his guitar slung low around his skinny jeans, was handed the microphone for a couple of songs, and former Stones' guitarist Mick Taylor joined the band to layer an intricate blues solo over 1969's Midnight Rambler.
He was the only surprise guest of the night, despite rumours that Adele or even Bruce Springsteen would make an appearance.
After 90 minutes, Sympathy For The Devil got a full airing, as flares turned the sky red and a mechanical phoenix rose from atop the Pyramid stage.
Jagger said: "We've been doing this for 50 years or something. And if this is the first time you've seen a band, please come again."
The encore was You Can't Always Get What You Want, and an extended, hyperactive take on (I Can't Get No) Satisfaction.
"Thank you very much Glastonbury," sang Jagger as the song reached its climax.
Fireworks lit up the farm and the band took a series of bows, while the audience continued to chant the riff to Satisfaction.
Meanwhile, at the Acoustic tent, the Bootleg Beatles played a Stones riff and commented: "Sign of a good band - you've got to know when to split up."
Earlier on Saturday proceedings had started with Malian musician Rokia Traore, whose upbeat blend of African roots, blues and jazz gave early risers a chance to dance off the fug of a late night.
A headliner at this year's Womad festival, Traore was offered a Glastonbury slot as a gesture of solidarity with Mali, where Islamist militants all but banned music in some areas.
Billy Bragg got into the spirit of the day by playing classic Stones track Dead Flowers during his set, while soul singer Laura Mvula welcomed the sun by breaking into a sing-a-long rendition of Bob Marley's One Love.
Speaking to the BBC afterwards, she said the cover had been suggested by her musical director, Troy Miller "whose last appearance here was with Amy Winehouse, so he knows what he's talking about".
Mvula, who only released her debut album Sing To The Moon, in March, said stepping out on the festival's main stage was overwhelming.
"Let me tell you something, there's nothing like it. A sort of nervousness I've never experienced before.
"It was like a mental battle - the goal was to get through it and enjoy as many moments as possible."
Other acts on Saturday's line-up included Elvis Costello, rap pioneers Public Enemy and psychedelic rockers Primal Scream.