Front row, from left: Jonathan Popp, Joe Lanza, Jared Craig, Samson Kohanski, and (seated on floor) Karl Baker Olson. Back row, from left: Mohit Gourisaria, Dan Whelton, and Sheldon Best. (Mike Lovett)

From the first snappy, stylized entrance of the eponymous students in “The History Boys,” it’s clear that Alan Bennett’s sharp play is in good hands at SpeakEasy Stage Company. Scott Edmiston directs this terrifically tight ensemble of eight young actors with precision and grace, and the four more seasoned performers who play their teachers bring their own rich expertise, too. It’s a marvelous Boston premiere of a wise and rewarding play.

Bob Colonna plays Hector, the aging English master whose sometimes eccentric methods (and occasional extracurricular fondling) run afoul of the ambitious headmaster at a working-class boys’ school in Margaret Thatcher’s England. Longing for the glory of sending his boys off to Oxford and Cambridge, the headmaster brings in a sharp young history instructor, Irwin, to polish their art of self-presentation - an art that Hector and his acerbic colleague Mrs. Lintott dismiss as mere glibness and flash.

Bennett puts all the elements of a classic schoolroom drama in play: the warring philosophies, the fight for young minds and hearts, the carefully diverse yet unified bunch of boys in the class. But “The History Boys,” which won the 2006 Tony for best play and also became a successful film, cannily sidesteps the dangers of cliche by - well, just by being so damn smart.

Yes, we may have seen such characters before, and it’s not hard to guess where their stories will take them. But Bennett gives them so much wit and insight that we can’t help wanting to go along. These sixth-formers - seniors, to us - love rugby and pop, but they also recite Auden and Hardy and Stevie Smith by heart. And the miracle is that Bennett makes us believe that they could.

That miracle would quickly fall flat, of course, if the cast couldn’t rise to the occasion. But SpeakEasy’s ensemble on the Roberts Studio stage unanimously does. A standout amid this universal excellence is Karl Baker Olson, who’s as heartbreaking in his recitation of Hardy’s “Drummer Hodge” as he is enchanting in his rendition of Rodgers and Hart’s “Bewitched, Bothered, and Bewildered.”

Bennett calls for that song in the script, along with the works of a few other artists from Edith Piaf to the Pet Shop Boys. But Edmiston and sound designer Dewey Dellay deserve special praise for their willingness to take such cues and build them into an integral part of the staging. Edmiston’s use of music is always surprising and fresh; here, it’s particularly rich in the way it underscores the emotions of a scene, clarifies the sometimes abrupt transitions, and generally gives the production a crisp, coherent structure against which its looser, wilder moments can naturally unfurl.

Much of the wildness comes from Colonna’s Hector, a shaggy, quietly furious old bear who knows that his way of teaching - of sharing the joy of knowing things just because they’re fun or inspiring to know, not because they’ll help you get ahead - is passing from the world. Colonna doesn’t soft-pedal Hector’s flaws (notably the habit of groping the boys when he gives them a ride home on his motorbike, a habit that has predictably dire consequences), but he also makes us see, with his fierce tenderness and a piercingly bright gaze, the passion for wisdom that this teacher passes on.

Chris Thorn gives Hector’s antagonist, Irwin, an appropriate smirk, but he also reveals the desperate insecurity beneath this glib contrarian’s polished exterior. His Irwin is entirely believable, whether pushing his students to favor flashy argument over deeply held belief in the exam room or, outside of it, betraying a surprising vulnerability to the most charismatic boy, Dakin (played, very charismatically indeed, by Dan Whelton).

Rounding out the faculty, Paula Plum delivers Mrs. Lintott’s most acid observations with devastating skill, and Timothy Crowe imbues the dim headmaster with a dithering impatience that’s funny but never cartoonish. And Edmiston’s frequent technical collaborators - Janie E. Howland, Gail Astrid Buckley, and Karen Perlow - further burnish the glow on this beautifully realized piece with detailed, skillful contributions in set, costume, and lighting design, respectively.

With both surface brilliance and inner warmth, this “History Boys” combines the strengths of both its battling masters. It’s one for the books.