‘Is that a catwalk?” says one woman, awaiting the arrival of this year’s Saturday night headliner. “It’s Beyoncé. Of course, it’s a catwalk,” snaps another. “Is she gonna bring any guests out? She doesn’t want someone to cramp her style, right?” says the woman. “Dude, her style is uncrampable,” comes the reply.

It’s true: Beyoncé’s style cannot be cramped. When she headlined Glastonbury for the festival’s 40th anniversary, in 2011, it was big for Beyoncé. Tonight’s performance, in the slot she was initially scheduled to do in 2017 (before announcing her second pregnancy), is big for Coachella.

She comes out dressed as a modern-day Nefertiti, revealing herself at the end of that catwalk behind scores of dancers led by a Black Panther mascot. “Ladies and gentlemen, welcome to Beyoncé homecoming 2018,” is the announcement over the tannoy, as a full marching band and orchestra take position on an enormous pyramid structure on the stage. Before the first song kicks in, Beyoncé has changed outfits into booty shorts and a jersey. “Coachella, y’all ready?” she says, and launches into Crazy in Love.

Thus begins a show that is somehow not just about Beyoncé. She makes it about far more than her or her career: it’s about black excellence, female power and the unrelenting possibility of self-belief. She has only a handful of white dancers among a reported 100. Her set is in thrall to soul, jazz, gospel, dance, melody and music itself. With her second song, Freedom, she creates a literal movement with her orchestra in motion; it feels like a march for purpose.

Tonight, Beyoncé plays political as fiercely as she plays feminist. During Sorry she hones in on the line “suck on my balls” with furious wrath. She flits between going hard and expressing sweet graciousness towards the audience during her addresses. The artistry of the transitions between songs, and the travel across her 20-year catalogue – combined with the sheer awe of scores of people on stage moving and playing in perfect unison – proves that Beyoncé is in a league of her own. She is the greatest of a generation, both a leader of a huge group and a solo star of unconquerable talent.

She’s also indebted to her musical past, and not just her own history. She splices Drunk in Love with Nina Simone’s Lilac Wine, elevated on a crane over the crowd. She has a go at husband Jay Z’s back catalogue, her orchestra alluding to Dirt Off Your Shoulder. There are classic hits from her early solo days, including Baby Boy; outings of the likes of Flawless and Don’t Hurt Yourself showcase her rock stardom with her third outfit change into black PVC. When she sings the infamous line “I woke up like this”, she turns to Coachella and asks: “How did you wake up this morning?”

The thing is, Beyonce did wake up like this. There is clearly a double entendre to the notion of wokeness, but the show doesn’t get woke at the expense of actually waking everyone up to the joy and togetherness of live performance.

Once she’s proved her mettle more times than necessary the thought of potential guests starts looming. She covers a smidgen of Dawn Penn’s You Don’t Love Me (No, No, No) and you wonder if it might segue into Destiny’s Child’s No, No, No, but not yet. There are a few hits to get through – Hold Up, Countdown, Check on It – and then Jay Z comes out for Deja Vu. After Beyoncé has spent almost an hour singing scorned female anthems about adultery, they display a heart-melting chemistry for one another. Moving into Run the World, however, she appears in army khaki, and you know it’s coming. She has to paid her dues to the thing that got her to this point.

It’s the reunion of Beyoncé, Kelly Rowland and Michelle Williams; destiny arrives with Destiny’s Child. Lose My Breath kicks off a throwback trio, including a meaty ecstatic rendition of Say My Name and then a fun-packed Soldier. For her final guest appearance, Beyoncé’s little sister, Solange, comes on to complete the family love-in, with a dance-off between the two that sings of sweet solidarity and universal sisterhood, before ending things with Single Ladies and Love on Top.

Mid-way through the set, Beyonce had turned to the crowd and, with total sincerity and humility, said: “Thank you for allowing me to be the first black woman to headline Coachella.” The crowd left the Polo fields with only one thing to say: “I was there.”

• This article was amended on Wednesday 18 April with a correction – Beyoncé referenced Nefertiti, rather than Cleopatra.