In many ways, the history of the theatrical avant-garde is simply the history of Western artists borrowing from the East. In the theater, particularly among formal experimenters, anything to the right of Iran was the go-to source: Peter Brook went to India, Julie Taymor built on techniques she learned in Indonesia, and Anne Bogart passes along Noh’s dramatic vocabulary whenever she teaches the Suzuki method. Whether you condemn it as cultural appropriation or praise it as cross-pollination, the result seems to be better art.

Such is the case with Brooke O’Harra’sTheater of the Two-Headed Calf. By staging their current production of Shaw’s “Major Barbara” as a (somewhat adulterated) Kabuki play, they have ratcheted up their own game to a new and welcome level. Ms. O’Harra does show a little overexcitement in her direction – a long stretch in the middle piles on extraneous videography, muddled narrative, and cheerful sloppiness that has hampered their work in the past. But by the time Act III rolls around, all is forgiven. By exploiting the La MaMa Annex to its fullest (with one revelatory, gasp-inducing scene change), and devising her own hybrid of Kabuki-meets-Drawing-Room comedy, Ms. O’Harra has finally found her stride.

Shaw, that cantankerous old Fabian, is nothing if not topical. In “Major Barbara” (written almost exactly 100 years ago), he gives us an ammunitions dealer as an antihero, a Salvation Army major as our heroine, and (here’s where the relevance wavers a bit) a Greek professor for a romantic foil. If it weren’t such a famous text, you’d think it was the new Soderbergh film.

Barbara (Heidi Schreck), her mother Lady Britomart (Tina Shepard), and her siblings are expecting a visitor – the absentee Andrew Undershaft, Barbara’s disgraced father. Driven from the home by his stern, unbending wife, Undershaft (Bob Jaffe) nonetheless treats his family with warm civility: He has come to settle their inheritances. But his children are hesitant to be his heirs, as Undershaft, with bubbling enthusiasm, forges most of the guns and ammunition in Europe.

Barbara, when we meet her, shines with her sense of purpose – her mother may complain that being a Major in the Salvation Army has made her bossy, but we only see hard work and gleaming righteousness. In other productions, Barbara can be played as shrill and overbearing; certainly Shaw would have cringed at her constant sermonizing. But Ms. Schreck plays Barbara as a more charming St. Joan, delightful in her faith rather than obsessed with “salvation.”

Her fiance, Adolphus (Mike Mikos), hasn’t got Barbara’s Christian zeal, reserving his devotion for her. Therefore Undershaft, who can match the Church’s preaching with his own capitalist dogma, finds converting Adolphus an easy challenge.

But when he sets his sights on destroying his daughter’s belief in the Salvation Army, he wins a Pyrrhic victory. Though he may not know it, his cold, pragmatic gospel has also lost him something: the last sparks of his daughter’s love.

As Religion dukes it out with Commerce, the actors move in little squatting runs, their hands formally on their thighs. When Lady Britomart screams at her husband, she waggles her tongue at him, making her face into a kind of dragon mask. Adolphus, bored during a scene that doesn’t involve him, paints his face with aggressive warrior make-up, and the local idiot Charles Lomax (David Brooks) pairs spectacles with the wide sleeves and flowing pants of a samurai.

Surprisingly, Shaw’s zingy dialogue survives the “translation” into Kabuki-style speech. The jokes still land, and much of the text is treated naturalistically, but when necessary, an actor will bark out a word like he’s striking a gong or break the word into sharp, percussive syllables. Justin Townsend’s stunning set also marries the styles seamlessly – though he employs waxed-paper screens, the shoji are printed with turn-of-the-century architectural details. When, in Act III, those panels are hoisted to reveal Undershaft’s weapons factory, Mr. Townsend creates one of the loveliest revelations of space La MaMa has seen in quite a while – a vista of red-lacquer gates and an infinite gray floor.

The conceit liberates the performers (Ms. Shepard should never do anything but Kabuki), and assists composer Brendan Connelly on to an incredibly successful score. Finding new ways to stretch in his faux-Japanese style – while he plays the woodblocks, his band plays sax and electric guitar – Mr. Connelly’s music goes from “spare but difficult” to spectacular. For everyone concerned, “Major Barbara” suggests a turning point. If the dragging second act worries you, have a little faith and stick around. If Barbara can do it, so can you.

Until September 16 (227 W. 42nd Street, between Seventh and Eighth Avenues, 212-719-1300).