Wings is not a play as much as a poem, one that conjures the fragmented and confused world of the stroke victim. In this thrilling production, it becomes something more – an act of theatrical magic that sends Juliet Stevenson flying into the high spaces of the Young Vic.

She plays Emily Stilson, a former aviator and wing walker, who is trapped by aphasia in a half-life between sleeping and waking, initially unable to speak or communicate, baffled and frightened but always courageous. "The storm will pass, always has," she reassures herself as the world turns to a blur around her. "I'm all right, getting better," she repeats like a refrain.

Perhaps because Arthur Kopit's play was inspired by his father's stroke, and the character of Stilson is a composite of the brave women he encountered at the Rehabilitation Centre he visited, Wings is powered by great imaginative empathy. We see the moment the seizure strikes – a simple blaze of light – and then follow Stilson into hospital, a place where she becomes convinced she has been imprisoned, tortured by an enemy for what purpose she cannot guess.

She imagines herself flying over the scene and what is utterly wonderful about Natalie Abrahami's sensitive production is that she actually does soar over the stage, spinning and turning in empty space, like a suspended rag doll at one moment, a graceful acrobat at the next.

The flying effects are by Freedom Flying and they are perfectly pitched; the wires are obvious, the movements Stevenson performs sometimes arduous. But the impact can be beautiful as well as clumsy. Combined with Kopit's words, you feel the sensations and suffering of a stroke victim are embodied.

Michael Levine's clever set also plays its part in evoking and making physical mental experience. A high raised platform, in the centre of two banks of seating, slides back and forth. When Stilson is lost in the sphere of her stroke, she is suspended in darkness. When she is terrified by what is happening to her, images on transparent curtains create the fractured state of her mind. As she finds gradual resolution, coaxed out of confusion by Amy, a sympathetic therapist (played with shining goodness by Lorna Brown) her flight is grounded. She steps on to the white side of the platform on tiptoe and begins to integrate with the real world.

All the cleverness of the conception, however, would be nothing without Stevenson's performance. It is both a considerable physical feat – all that twisting and turning – but crucially an emotionally complex one. She perfectly catches every beat of Stilson's feelings, conveying universes in a pause, or a fleeting expression of hope or doubt, or ferocious anger.

Best of all she captures the character's pluck, her sense of adventure. When she struggles to remember what a toothbrush is, what it is called, what it is used for, she shows an almost unbearably touching mixture of insouciance and determination. It is moving and truthful – and it flies straight to the heart.

Wings runs at the Young Vic until 4 November.