If, as Pauline Kael remarked, Fatal Attraction is the worst dating movie ever made, then Boy Gets Girl has to be the all-time no-no of a theatre treat for a couple on a blind date.

Rebecca Gilman's new play opens with the amusingly awkward and gaffe-strewn initial encounter between Katrin Cartlidge's beautifully acted Theresa, a smart, literate journalist on a New York cultural magazine who is wedded to her work, and Tony (Demetri Goritsas) an attractive, all-American computer programer. They have been set up by a mutual acquaintance whose perspicacity must be nil, because it takes only one dinner engagement to demonstrate that Theresa would have far more fun in a nunnery than in the company of this shallow chauvinist.

She puts a stop to their meetings, and that's when the flowers, the unannounced visits, the accusations that she is repressed and the ceaseless (increasingly filthy) phone messages begin. Without ever losing its sharp wit, the play expands into a truly chilling and affecting study of human isolation and vulnerability in big cities. Sexual stalking is, of course, a favourite subject of the low-brow, made-for-TV movie. Oddly, Boy Gets Girl is sometimes at its weakest when it most consciously distances itself from that genre.

Gilman is a tidy and fair-minded writer – too much so. For example, there are some very funny scenes where Theresa interviews an elderly soft-porn director (Karl Johnson) who has become a cult figure. But you just know that this monothematically breast-obsessed character, who has made a career out of "objectifying" women, will turn out to be Tony's antithesis, and the most practically helpful friend to her by the end. You can hear the intention clicking in the background. And I could happily dispense with some of the neatly explanatory speeches, as when Mercer (Jason Watkins), a well disposed colleague who wants to write an article about Theresa's predicament, confesses to their editor that it's not just Tony who has had ugly sexual fantasies about her. Oh God, you think, not the old we-are-all-guilty shtick.

Boy Gets Girl has, however, a strength of poignancy and humour that helps it survive such blemishes. Ian Rickson directs the piece with his characteristically sure, musical feel for structure, and he draws from Ms Cartlidge a splendid central performance. It's unbearable that this tall, bonily handsome and winningly self-reliant woman should be evicted from her proud, bookish seclusion and left dependent on the kindness of colleagues.

Our sense of his creepy stranglehold on her life only heightened by the fact that he becomes an invisible presence in the play, Tony had earlier charged her with fearing intimacy. His actions have the ironic effect of making that true. There's an excellent moment when the unnervingly frank female police detective (Lolly Susi) says that she likes to respond to people as individuals, in individual ways. But Theresa finds it comforting to think that the procedure is a standard one. That way, she feels less alone.

Meanwhile, the dreadful violation of her privacy is brought home by a lovely, achingly sad touch. Cleaning up the apartment that Tony has trashed, her male colleagues come across a cat calendar on which, each month, there's a little dot with a circle round it. They puzzle over it for a second before subsiding into embarrassment. She doesn't even have a cat, still less the prospect of a child.

As with newspaper articles that effectively teach you how to make bombs, there's something a bit dangerous about this piece. You learn the simple steps by which you can totally destroy a person's life. But, then, art should be risky at the Royal Court.

To 15 Dec (020-7565 5000)