The Oxford quintet emerged, bathed in white light, to the haunting piano refrain of Daydreaming, from last year's A Moon Shaped Pool album.
Two hours and 25 songs later, they closed with Karma Police, singing: "For a minute there, I lost myself."
It felt like a perfect metaphor for the band's power to transport an audience.
The performance came on the 20th anniversary of Radiohead's first headline set at Glastonbury.
That show, which took place just weeks after they released OK Computer, has often been called the festival's best ever.
However, frontman Thom Yorke recently told BBC 6 Music he had been on the verge of walking off the stage, after the band's monitors exploded, meaning they could not hear each other.
"I just went over to Ed [O'Brien, guitarist] and said, 'I'm off mate, see you later,'" he recalled.
"He turned around and went, 'If you do, you'll probably live the rest of your life regretting it.' I went, 'Good point.'"
There were no such problems on Friday night, as the band embarked on a career-spanning set that held their experimental and anthemic qualities in perfect balance.
Airbag was thrilling, Pyramid Song devastating, and Everything In It's Right Place a pulsing, twisted Radiohead version of a club classic.
They even pulled out the much-maligned Creep - the angsty, teenage anthem that gave them early success, but became a millstone around their necks as they matured into a fearlessly experimental art-rock outfit.
Things got political - briefly - during No Surprises, where the lyric "bring down the government, they don't speak for us," elicited a huge cheer from the festival's left-leaning audience.
As the song ended, Yorke commented: "See you later, Theresa. Just shut the door on your way out."
That aside, the frontman rarely spoke during the set, except to thank Glastonbury organisers Michael and Emily Eavis "for having us at your lovely farm today".
"Thank you very much for coming to this field to listen to us this evening," he added during the encore.
"Probably we'll see you in some other fields over the weekend."
Radiohead were preceded on the Pyramid Stage by indie-dance band The xx, whose spiralling, hypnotic songs soundtracked dusk on Worthy Farm.
Immediately before them, rock group Royal Blood celebrated with champagne on stage as their second album, How Did We Get So Dark, entered the charts at number one.
Speaking to the BBC, singer Mike Kerr said the band were bowled over by the two events converging.
"We definitely have a sense that this is a one-off thing. It's something I'll look back on as a very special time."
Elsewhere on Friday, there were sets from Sleaford Mods, Clean Bandit, Dizzee Rascal, The Lemon Twigs and Flaming Lips.
On The Other Stage, pop star Lorde began her set "trapped" inside a clear plastic box that tilted back-and-forth above her band.
Once she emerged onto the stage, she dedicated a recently-released song, The Louvre, to anyone in the audience who was harbouring a secret crush.
"Shut your eyes and listen to the song, and just will it to happen," she said. "Maybe they will kiss you tonight. Who knows?"
Actor Bradley Cooper appeared on the Pyramid Stage to film a scene for his new movie, a remake of the musical A Star Is Born.
He then introduced Kris Kristofferson, who was watched from the side of the stage by fellow Hollywood star Brad Pitt.
Johnny Depp also joined the singer-songwriter, who was 81 yesterday, playing guitar on one of the songs.
Depp caused controversy on Thursday, as he joked about assassinating Donald Trump during an appearance at Glastonbury. He has since apologised.
Former footballer David Beckham also made his first visit to Glastonbury, to help organiser Michael Eavis launch a new social housing project.
He planted a tree at the development in the nearby village of Pilton, before heading to the event with his 18-year-old son, Brooklyn.
If they stick around until Saturday, they will see acts including Stormzy, Katy Perry, Liam Gallagher and headliners the Foo Fighters.
Labour leader Jeremy Corbyn will also appear on the Pyramid Stage to introduce US rap act Run The Jewels.
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Absorbing, challenging and achingly beautiful - Radiohead delivered a typically Radiohead sort of set for Glastonbury's opening night.