A Streetcar Named Desire is the best known play of the mid-20th century and it is also (and not unrelatedly) known in an exceptionally famous version. Marlon Brando’s Stanley Kowalski in Elia Kazan’s 1951 film version, recreating his original stage performance, has never been remotely rivalled and the fact that his Blanche DuBois was Vivien Leigh, Scarlett O’Hara herself, and that Brando seems to have wrested a performance from her by sheer force of histrionic danger greater than anything she had done before is the stuff of a legend so everlasting as to make most stage productions look like footnotes.

So it’s all the more remarkable that Kate Cherry’s production for the Black Swan Theatre Company in Perth with Sigrid Thornton as Blanche is such a glowing, vivid, beautifully paced piece of work, fresh and surprising at nearly every point. And Sigrid Thornton as the damaged and damaging Southern belle is a revelation. She finds vast subterranean countries of madness and sweetness in the role. She commands the stage with a swooping grace, at once predatory and coy and she succeeds at the same time — and in a way that Cate Blanchett, great actress though she is, did not equal — in creating an utterly coherent and credible characterisation of a particular person.

There is none of Blanchett’s grand anthologising of unco-ordinated epiphanies here. Thornton’s is a Blanche with a deep and dangerous strain of madness and she is also winsome, bitchy, savage with a great capacity for snarling energy, for flirtatious charm and for the purest ice. She keens like a siren, she coos like a girl, she finds great gulfs of feeling in a lower register that seems to come from nowhere and is more indicative of the mature woman overripe to the point of sickness than any harsh exposure from an overhead electric light.

This is a masterly performance with a visceral rawness and power. It should be seen around the country. It shows what command Thornton, the best known television actor in the country, in fact possesses as a stage actress but more particularly it has an authority and an edge that we rarely see in the classic modern American repertoire. And Kate Cherry’s production supports at every point with great, glowing dabs of 1950s colour — the costumes and set by Christina Smith are very stylish — but also with a heightened sense of claustrophobia, the mere two rooms that form the boxing ring of one of the greatest exhibitions of sexual tension in the whole of drama. It’s true that Nathaniel Dean’s Stanley doesn’t rise to anything like the same level as Thornton’s Blanche but it’s an adequate performance in a production that shows Kate Cherry understands Tennessee Williams’s idiom like the back of her hand.

For once we saw the bump out, the last not the first night, of this Streetcar. The audience on this final Friday night were sunny and casual, many of them were young. If Janet Holmes à Court and Rio Tinto had come for a last glimpse of this bright star of a production, we caught no glimpse of them. But it was an alert audience and Kate Cherry’s production, with its rich pictorialism and its superb pace over the course of a very full text, taking the play to the length of a Shakespearean tragedy, held them spellbound.

The last-night party afterwards was at the appropriately named The Bird (the playwright’s nickname) and we spent our brief, noisy time there shouting conversationally at Kenneth Ransom — Cherry’s husband who is to play Othello next year — and at Sigrid who was looking a bit like a queen who had just fought a war.

Kate Cherry’s Streetcar is essentially Thornton’s show because this does not, as Brando’s and Leigh’s did, come within cooee at least of being an equal histrionic battle. Perhaps if Heath Ledger had played Stanley like a nightmare animal instantiation of Blanche’s tilt for boys, perhaps if a younger Russell Crowe had bent the role to the sweep of his imperium and his sense of sound and fury, we might have got this. But Nathaniel Dean’s Stanley is accurate enough in conception (what he accentuates and emphasises is right, he never misinterprets but he sketches danger as a postulate, he cannot embody it with a headlong bull-like lunge).

It matters, but, oddly enough, it is not fatally damaging, because Cherry and Thornton are so deliberate and so assured in their frontal classically compositional evocation of the fullest range of the misbegotten beauty and squalor of Blanche’s disarray that it is enough to have the apelike demon Thornton conjures up in her mind with its basis in Dean’s earthbound, intelligent, slightly oafish Stanley.

Jo Morris’s Stella is good and Luke Hewitt’s Mitch never hits a wrong note even if his manner is a bit old. But the production as a whole has a superb, long paragraphed musicality like watching one of the great Germans like Furtwängler conduct Wagner, not with the occasional effect but for the monumentality of the movement.

It’s a sizzling, cinematic New Orleans Cherry conjures up, everywhere alive to the tang of sensuality and the faint lick of darkness and sexual perverseness. It’s marvellous that the young collector is played with a golden boyishness by the 17-year-old Callum Fletcher — and what a leitmotiv of the dead gay husband.

Thornton kisses him like a girl, like a mother, like a serpent of old Nile. Her performance throbs with sexual longing, with a piteous, never quite controlled erotic power and with an utterly bare and brave mental distress and frailty. This is the sort of acting that makes you weep at the sweep and strangeness of its authenticity. The vowels like poison treacle, the girlish body ageing and exposed like the cage of a spirit at once beautiful and awry. The final ‘comfort of strangers’ moment when they take Thornton’s Blanche away is violent, abrupt, full and overflowing with pity and terror.

There is talk of this production going to Brisbane. It should also be seen in Thornton’s hometown Melbourne. How odd that it should be patently superior to the performance that inspired Woody Allen’s Blue Jasmine. It’s Thornton’s and Cherry’s Streetcar that shows how Williams changed the very idiom of Hollywood.