Five stars for The Lost Daughter

middle-aged professor who once abandoned her family, a little girl who wanders off on a beach and even that girl's missing doll, which when found spurts filthy water from her mouth – there are many lost daughters in this eloquent adaptation of Elena Ferrante's 2008 novel, along with one eye-opening find: Maggie Gyllenhaal as a filmmaker with a true artist's vision.

Plenty of actors who turn to directing can surround themselves with a first-rate crew, and come through with perfectly competent results. Fewer can do what Gyllenhaal accomplishes here. In her first film as writer-director, she transforms Ferrante's often enigmatic fiction into a drama that lives dynamically on screen.

Gyllenhaal completely understands the appeal behind the cult of Ferrante, whose books – including My Brilliant Friend and the three other Neapolitan novels, which arrived after The Lost Daughter – probe the emotions beneath the lives of ordinary women. She also had the judgement and good fortune to cast Olivia Colman, who brings a vibrant presence and all her powers of subtlety to the role of Leda, a professor on holiday in Greece. Leda's at-first inexplicable obsession with a big, boisterous family she sees on the beach, especially the beautiful Nina (Dakota Johnson) and her often clingy little girl, leads to memories of her own fraught past as a mother and a daughter.

Colman can make Leda simply driving a car seem dramatic, as the expression on her face quietly captures the emotional turmoil she tries so hard to contain. And Gyllenhaal can turn an image of rotting fruit into a jump-scare. Nuanced though it is, the story is always engaging and full of unexpected turns.

The soul of the film exists in the small exchanges and tensions between characters

The setting was transplanted to Greece, rather than the novel's location of Italy, so the film could be shot there. Leda is now British and the family on the beach is from Queens, New York, with Greek roots. And voila – the actors' accents are neatly accounted for. Apart from such small tweaks, the film perfectly mirrors the graceful flow and underlying tension of Ferrante's story. As Leda says in the novel, "The hardest things to talk about are the ones we ourselves can't understand," a line that might be a guiding principle for the film, whose entrancing narrative lures us into Leda's world with all its residual guilt and self-questioning.

She arrives with a suitcase full of books for a quiet working holiday, and is at first annoyed by the noisy arrival of the American extended family. But Colman and Gyllenhaal create an intentionally queasy feeling when Leda spots Nina among them. Why is she so taken with that young mother and daughter? The answers arrive gradually, in flashbacks with Jessie Buckley as the prickly younger Leda.

The story has its moments of suspense, especially when Nina's child wanders off from the beach. But the soul of the film exists in the small exchanges and tensions between characters. No motive or interaction is simple, the complications expressed sometimes in glances, sometimes in words. Dagmara Domińczyk sharply defines Nina's brash, pregnant sister-in-law, Callie, who is by turns benign and intrusive. "Children are a crushing responsibility," Leda tells her, hardly the diplomatic thing to say to a woman expecting her first child, but the comment – maybe wilfully hurtful, maybe thoughtless – is true to Leda's character. Johnson, in her best performance by far, poignantly captures Nina's jumpiness and ambivalence as a woman with nothing to complain about (so she says), except an exhausting child who makes her feel trapped in her own existence. Even the supporting characters have secrets and mysteries. Paul Mescal from Normal People plays Will, an assistant on the beach whose friendship with Leda is slightly unsettling. Ed Harris plays the attentive caretaker of the apartment Leda rents, who may be attracted to her, or simply lonely, or possibly toying with her in some way. The missing doll leads to subterfuge and suspicion. And we begin to wonder whether Leda has tipped over from ordinary to something more disturbed.

In the flashbacks, chronologically but piecemeal, we come to see how Leda became who she is. Buckley's fierce character is a woman whose passion and professional ambition are a bad fit for her domestic life with her husband and two small daughters. She is never uncaring, but she slams doors, snaps impatiently at her children, and faces a dilemma when she meets an attractive colleague (Peter Sarsgaard). Like Ferrante, Gyllenhaal surfaces uncomfortable questions, including: how far can a woman defy society's expectations and her maternal role in the interest of saving her own sanity?

Off-screen Gyllenhaal has surrounded herself with other first-rate collaborators, especially Hélène Louvart, whose cinematography captures the bright sun and glimmering night streets, and takes us inside an exuberant town dance where Leda lets loose to Bon Jovi's Livin' on a Prayer.

You don't have to know or even like Ferrante's writing to appreciate this colourfully realised world. But it's notable that Ferrante herself trusted Gyllenhaal with her novel, supporting her choice in a short newspaper column that said: "There's something much more important at stake than this instinct to protect my own inventions. Another woman has found in that text good reason to test her creative capacities." And since the film first appeared on the festival circuit, winning best screenplay at Venice, Gyllenhaal has said in interviews that she wrote a letter to the author describing her idea for the film, and that Ferrante agreed only on the condition that Gyllenhaal herself direct it. That stipulation was a generous act that protected a first-time filmmaker from the risk of having the project taken away from her, but it was also a shrewd move on Ferrante's part. It preserved a vision of The Lost Daughter that now stands on its own as a dazzling, beautifully realised film.