Midway through “The History Boys” a professor discusses the patriotism of World War I poets with eight grammar school students. The boys, in response, casually quote a lengthy poem by Philip Larkin.

These promising sixth-formers – the British equivalent of high school seniors – have found themselves in a pedagogical tug-of-war between two professors. One, Mr. Hector (the riveting Richard Griffiths), has long encouraged learning for learning’s sake; the other, a newcomer named Mr. Irwin (Stephen Campbell Moore), focuses on how to “game” the system and increase the boys’ odds of getting into Oxford or Cambridge.

Here’s the thing: The poetry discussion, which also touches on the precipitating causes of World War I, happens in Mr. Irwin’s class. Any story in which this is considered a step down in educational sophistication has its work cut out for it with U.S. audiences. But Alan Bennett’s aching play, purged of any sentimentality by director Nicholas Hytner and an extraordinary ensemble cast, tackles with bracing universality the joys of becoming smarter and the pains of becoming wiser.

“The History Boys” is an unexpectedly moving mixture of intellectual verve and sexual angst. Mr. Bennett, a prolific British playwright whose work hasn’t been seen on Broadway for more than 30 years, has written an array of juicy scenes rich with epigrammatic quotes. (Western culture is so fascinated with archaeology, Mr. Irwin suggests, because “it’s the closest history comes to shopping.”)

But most of the memorable lines are as touching as they are clever. A disproportionate number of these come from Ms. Lintott (the splendid Frances de la Tour), a fellow old-guard instructor and the lone woman on the stage. “One of the hardest things for boys to learn is that a teacher is human,” she tells Mr. Irwin after a revealing student-teacher conference. “One of the hardest things for a teacher to learn is not to try and tell them.”

The flaws that make these professors human go way beyond an eye toward expediency, though. “The History Boys” is emphatically not “Dead Poets Society” or “Goodbye Mr. Chips,” where the professor’s only real failing is expanding the minds of his pupils too much, loving them too much. Well, actually, loving the pupils too much is the problem. Mr. Hector, in the sort of plot point that occasionally renders the British incomprehensible to Americans and vice versa, is a pedophile.

He has his scruples, of a sort: His fumbling attentions are confined to rides on his motorcycle, and the one underage pupil is spared. Unlike “Doubt” or “Festen,” two plays currently running that focus on the crippling effects of such behavior, “The History Boys” shrugs at Mr. Hector’s gropings with a cavalier – and very British – shrug.

And while this has dire consequences for Mr. Hector, the students – who voluntarily take turns on the bike – show little, if any, adverse effects. This nonchalance is a much tougher sell in America, and I suspect the public response would be very different if the play were titled “The History Girls.” But Mr. Bennett does justice to Mr. Hector’s many gifts, as well as his failings, and Mr. Griffith’s layered, robust performance goes a long way toward contextualizing without excusing his actions.

The titular octet is beyond reproach in terms of sensitivity and comic timing, although Jamie Parker as the piano-playing Scripps and Russell Tovey as the (relatively) dim athlete Rudge are first among equals. They created the roles in London, and their deep comfort with the play is apparent from the very first scene. (They have also been entrusted with moving Bob Crowley’s terrific, richly detailed schoolroom sets on and off the stage.)

In fact, the only false performance in the entire play comes from an over-the-top Clive Merrison as the conniving headmaster. This is more than offset by exquisitely calibrated work from Messrs. Griffiths and Moore, and by Ms. de la Tour’s scene-stealing supporting work.

“All knowledge is precious whether or not it serves the slightest human use.” This quotation comes from A.E. Housman, who has served as a sort of exemplar to Mr. Hector, for better and for worse.

Is it a coincidence that Hector’s plan for life after teaching includes traveling to Shropshire, the home of Housman’s immortal doomed lad? Or that Tom Stoppard, a clear influence on Mr. Bennett here, himself celebrated Housman in “The Invention of Love,” another elegiac tale of repressed homosexuality within British academia? Or that a punch line in “Invention” involves a surviving fragment of Aeschylus in which Achilles learns of his lover’s death at the hand of … Hector? Or that these sorts of seemingly useless tangents are what both professors Irwin (for their out-of-the-box spontaneity) and Hector (for their sheer uselessness) adore?

Near the end of Act I, Mr. Hector and Posner (Samuel Barnett) – the youngest boy, the one left unmolested – parse Thomas Hardy’s “Drummer Hodge.” In the process of a gentle, beautifully staged discussion of the poem, Mr. Hector is asked how old Hardy was when he wrote the poem. “About 60. My age, I suppose. Saddish life, though not unappreciated.” Rarely are a character’s hopes and fears addressed so succinctly, and yet the line is still completely in service to the literary discussion taking place.

Later in the same scene, Hector tries to convey the decades-swallowing elation that comes from stumbling upon a thought or feeling in literature that feels unique to your own temperament: “It is as if a hand has come out and taken yours.” Mr. Hytner has choreographed Messrs. Griffiths’s and Barnett’s movements to the point where, as Mr. Hector reaches for the book, his hand comes within a millimeter of brushing Posner’s.

It’s not entirely clear – not to the audiences and probably not to either character – whether they meant to come this close to touching, or wanted to, or even should. The moment is inconclusive, honest, uncomfortable, and more than a little sad.

“The History Boys” has almost a dozen such moments. And even when the occasional bit of schoolboy banter stretches a bit too far or the boys’ sexuality threatens to derail the play’s balance, Mr. Hytner’s superb cast sees to it that Mr. Bennett’s hand reaches out again and again, confidently enveloping the audience in its rigorous, quietly devastating grip.

Until September 3 (235 W. 44th Street, between Broadway and Eighth Avenue, 212-239-6200).