“Saturday Night Live” vet Jason Sudeikis makes a convincing stage debut as an unorthodox New England prep school teacher in the world premiere of “Dead Poets Society,” a new play based on the popular film. It’s just opened at the Classic Stage Company.

I cherish the 1989 movie, which starred Robin Williams as a teacher at, and alumnus of, Welton Academy—or, “Hell-ton,” as generations of students have sarcastically called it. Aside from Williams, the film was an early showcase for the skills of Robert Sean Leonard, Ethan Hawke and Josh Charles.

You have to feel for an actor who would dare follow in Williams’s footsteps as John Keating, a colorful academic who encourages his students with a cry of “Carpe diem!” Sudeikis turns out to be an excellent fit, not mimicking the late comedian, but bringing his own mischievous charm and wicked wit to the part.

This production is written by Academy Award winner Tom Schulman, and adapted from his own screenplay.

Director John Doyle, the CSC chief and respected Sondheim interpreter, has, as is his way, stripped down “Dead Poets” to the essentials. The set at the tiny CSC is a wall of books as backdrop, and not much else. The schoolboys remove books from the shelves to form chairs … when they’re not ripping out pages, on the advice of their teacher.

The half-dozen actors portraying Keating’s malleable charges perform double-duty as ushers, distributing programs before the start of the 2-hour show. We meet them as they, and then Sudeikis, whistle and sing Welton’s school song.

The students eventually reanimate the poetry-worshiping society of the title, an old club they learn about when they find the yearbook from Mr. Keating’s graduating class. “Full membership required a lifetime of apprenticeship,” Mr. Keating explains, when the boys press him. “The living were simply pledges.”

The two teens around whom most of the story turns are Neil Perry (Thomas Mann), whose stern father (Stephen Barker Turner) becomes furious when his son takes an interest in acting; and Todd Anderson (Zane Pais), a stuttering, withdrawn lad whose personality emerges when Mr. Keating introduces him to Whitman and the like.

Mann and Pais both bring sensitivity to the stage. Cody Kostro is equally on point as their rebellious classmate Charlie Dalton, who will later adopt the personality of “Nuwanda,” painting an Indian symbol for virility across his chest. The main villain of the story is headmaster Paul Nolan (the excellent David Garrison, a CSC regular).

So many properties these days get a stage treatment because producers know some patrons will buy tickets just because something is familiar. In this instance, “Dead Poets Society” stands on its own as an effective work of drama, even for a generation of audiences who may have no idea what preceded it.

“Dead Poets Society,” through Dec. 18 at CSC, 136 E. 13th St. Tickets: Extremely limited. Call 866-811-4111 for inquiries.

Follow Robert Kahn on Twitter@RobertKahn