Sarah Greene, Daniel Radcliffe and Pat Shortt during the Broadway opening night of “The Cripple Of Inishmaan.” (Photo by Andrew Toth/Getty Images)

NEW YORK–In his previous Broadway ventures, as the disturbed youth who blinds the horses in “Equus” and the sneaky trainee who dupes the CEO in “How to Succeed in Business Without Really Trying,” Daniel Radcliffe seemed a man on a mission: to learn how to translate the galvanizing impact of his presence on film into a more intimate transaction for the stage.

Now, at last, with his soulful work in the Broadway premiere of Martin McDonagh’s “The Cripple of Inishmaan,” one can say with satisfaction and confidence: Mission accomplished. Radcliffe’s doe-eyed turn as the physically contorted Billy of the title is by far his most completely realized dramatic performance yet, evidence of a purity of commitment to the theater and a resultant growth as an actor.

His portrayal, too, is knitted seamlessly into director Michael Grandage’s splendid, London-born incarnation, as fine as anything presented on Broadway this season and as rewarding as the version by Ireland’s Druid theater that visited the Kennedy Center in 2011. These two productions of McDonagh’s cleverly drawn, 1996 tragicomedy happen to share an actress, the marvelous Ingrid Craigie, playing one of Billy’s aunties, Kate, who in times of anxiety talks to a stone. In both versions, her contribution is emblematic of an ensemble that can expertly wring both the wit and pathos out of McDonagh’s portrait of an Irish backwater, where an oppressive level of familiarity breeds an uproarious brand of contempt.

The newer production, which had its official opening Sunday night at the Cort Theatre, revolves on a superb turntable set by Christopher Oram that imbues the desolate interiors and landscapes–a country store, a craggy shorefront–with the brooding characteristics of the people who eke out marginal livings there. The setting is Inishmaan in the Aran Islands, the windswept, rocky outcroppings off the west coast of Ireland, where, in 1934, the famous documentarian Robert Flaherty is filming his soon-to-be-classic film, “Man of Aran.”

News of the movie being made on a nearby island is conveyed by the seemingly craven Inishmaan gossip, Johnnypateenmike, portrayed here as a Dickensian bottom feeder by the terrific Pat Shortt. The bookish, orphaned Billy–whose disability has earned him the demeaning nickname Cripple Billy–goes on an unlikely quest. He slips away from the shabby store run by the unmarried sisters who’ve raised him, Craigie’s Kate and Gillian Hanna’s Eileen, to see if he can get cast in the film and make his way to Hollywood.

The outlandishness of Billy’s dream is a reflection of the paradoxes rampant in the natures of Inishmaan’s denizens, people capable of pivoting at any moment from cruelty to kindness and back again. Each and every one of them is as unpredictable as the weather, including Babbybobby (the sterling Padraic Delaney), the rugged boatman who agrees to take Billy to the film set and Slippy Helen (a wonderful Sarah Greene), the island beauty with a taste for bullying, and whom Billy fancies.

McDonagh is a master-frustrater, and I mean that in a good way. He takes our expectations in his manipulative fists and crushes them, over and over and over. It’s incumbent in “The Cripple of Inishmaan” that we get our hopes way, way up for Billy, and Radcliffe, with Grandage’s excellent guidance,  sees to it that we’re bound to this character through his compassion and high intelligence, and that we ride the waves of his joys and disappointments along with him. You feel, too, with this performance that Radcliffe truly has left Harry Potter behind–a bonus sensation on an evening filled with the pleasures of drama played well-nigh to perfection.

The Cripple of Inishmaan, by Martin McDonagh. Directed by Michael Grandage. Sets and costumes, Christopher Oram; lighting, Paule Constable; music and sound, Alex Baranowski. With Conor MacNeil, June Watson. About two hours 15 minutes. Tickets, $27-$275. At Cort Theatre, 138 W. 48th St., New York. Visit or call 212-239-6200.