This is possibly the most joyous, life-affirming film ever to be made about terminal disease. The Australian director Shannon Murphy’s feature debut, Babyteeth, is a marvel; the kind of skittish, reckless film-making that makes you want to rush headlong into bad decisions and savour every last messy moment of the fallout.

Since her cancer diagnosis, 16-year-old Milla (Eliza Scanlen) has become insulated. Her home life is loving, but cushioned by the kind of parental concern that suffocates as much as protects.

Then, while she is waiting for the morning train to school, Moses (Toby Wallace) crashes into her life. Rattling and scattershot with pills and chemical energy, he’s any parent’s worst nightmare. But Milla takes one look at his stringy limbs and homemade tattoos and makes her choice. The carriage doors sigh shut, the train leaves without her. And Milla stays on the platform, with this chaotic boy who pinballs into her personal space and peels off his shirt to stem her nosebleed. But there’s an added layer to this sliding doors moment of sexual awakening. Deep down, Milla knows that, for her, the opportunity to grab life and live wild is rapidly closing. And it doesn’t get much wilder than Moses.

For Milla, it’s a headlong rush into first love. Like her character, Scanlen makes every moment count – a single loaded look, which sweeps between her parents and Moses, contains a symphony of emotions, starting with adolescent defiance and ending with an ache of uncertainty and longing.

But what draws Moses, initially at least, is the realisation that his new friend’s family home is an all-you-can-eat drugs buffet. In addition to Milla’s cancer medication, there are the prescription pills that smooth the edges off her highly strung mother (Essie Davis): rich pickings for an enterprising addict. Meanwhile, Milla’s parents have to balance the urge to chase Moses away for ever against the knowledge that he makes their daughter more alive than she has been for months.

The screenplay is adapted by Rita Kalnejais from her own play, but the storytelling here does not feel rooted in the theatre. Murphy grasps every means of cinematic expression available to her. Her use of colour sings, subliminally reinforcing this unlikely bond between a dying girl and a junkie: the way that Milla’s teal wig matches the too-big shorts that engulf Moses’s unsteady twiglet legs; on a stolen night out, their lilac shirts accidentally harmonise, like a shared private joke. The connection between them is real and tangible. The symbiosis of craft and character extends to the dancing, uninhibited camera and to the editing, which has a teenager’s headlong impatience and lurching attention span.

But what really elevates the film is the use of music – crucial, given that both Milla and her mother are musicians. Murphy rejects the kind of handholding score that would wring every last drop of sentiment from the material. Instead, she assembles a thrillingly eclectic soundtrack, which embraces everything from a string quartet version of the Stranglers’ Golden Brown, to Vashti Bunyan’s twinkling Diamond Day, to Sudan Archives’ euphoric Come Meh Way, with its whirling harmonics and percussive violins. I particularly loved the use of a children’s choir version of the traditional sea shanty Santianna, which accompanies Moses’s rock-bottom dash to the home of his estranged mother. Crystalline and pure, it’s such an unexpected choice, so utterly right for the scene that plays out. There’s a fearlessness to Murphy’s film-making, a slightly wayward, maverick spirit. I can’t wait to see what she does next.

• Babyteeth is on release in cinemas now

• The caption to the main image accompanying this article was amended on 17 August 2020 to correct the spelling of Eliza Scanlen’s surname.