Jonathan Hadary as Tevye and the company of ‘Fiddler on the Roof’ at Arena Stage. (Margot Schulman)

Tevye the milkman has been played by countless performers since “Fiddler on the Roof” began its long Broadway history 50 years ago, yet at Arena Stage, Jonathan Hadary acts the part like it was written yesterday. Hadary’s Tevye is funny but not a buffoon, warm but not schmaltzy — and, boy, does he connect to his increasingly rebellious daughters. He is the genial, breakable heart of a production that does justice to one of the gold-standard American musicals.

The ease of this “Fiddler” is a pleasant surprise, for director Molly Smith’s record with Broadway chestnuts has been spotty ever since she inaugurated her near-annual fling with “South Pacific” over a decade ago. Smith scored a major popular success with the praised “Oklahoma!” as she led Arena into its expensively expanded new complex in 2010, but misfired afterward with “The Music Man” and “My Fair Lady.” Both were distractingly designed, and “My Fair Lady” was inexplicably underperformed.

You can also argue that no matter how many tickets Arena sells, consistently peddling mainstream musicals is a questionable mission for a company so deeply branded as a pioneer of the not-for-profit, anti-Broadway regional theater movement.

Yet this “Fiddler” persuasively makes its case as it merrily stamps across the in-the-round Fichandler stage. It shapes up as Smith’s most solid musical to date. Nothing really goes wrong, and an awful lot goes right.

Perhaps as never before, Smith simply trusts the material. And why not? Joseph Stein’s book, based on Sholem Aleichem’s stories about the late-19th century shtetl life of European Jews, takes a winningly wry tone but bows to the brutal reality of pogroms. Jerry Bock’s score is a wonder, from the ebullience that turns pensive in “Matchmaker” to religious undercurrents that murmur in “Sabbath Prayer” and swirl in “To Life.” And Sheldon Harnick’s sensible, memorable lyrics couldn’t fit more gracefully with the tunes. (A beaming Harnick, 90, was on hand for Wednesday’s opening.)

Tony-award nominee Jonathan Hadary makes his Arena Stage debut as the character Tevye in "Fiddler on the Roof." Directed by Molly Smith and lyrics by Sheldon Harnick. Through Jan. 4. (Courtesy Arena Stage)

Smith doesn’t overthink any of this. She confidently guides the action on Todd Rosenthal’s simple wooden plank stage, a plain rustic look that includes a spiral of planks overhead, where the rooftop fiddler initially appears. (Paul Tazewell’s peasant costumes are in the same unassuming mode.) The pleasures add up quickly in the first act as Hadary’s quick-tongued Tevye amusingly questions God, so neatly summed up in “If I Were a Rich Man,” and guides us through his poor shtetl, Anatevka.

Smith makes understated use of the space for the reverent “Sabbath Prayer,” but she also has a dazzling trick up her sleeve for Tevye’s delirious dream sequence. Parker Esse ably tailors Jerome Robbins’s famed original choreography, bottle dance and all, for the in-the-round setup: The zesty group dancing is familiarly earthy and athletic, with lots of celebratory circles. It’s even charming as Michael Vitaly Sazonov’s Perchik (the bookish young revolutionary) guides Hannah Corneau’s Hodel (perhaps the strongest-willed of Tevye’s daughters) on a sudden light-footed romp.

With its mandolin and clarinet accents, musical director Paul Sportelli’s 10-piece orchestra is largely up to the task of buoying the large cast. Vocally, there are no knockouts in the cast, but “Fiddler” has never been a belters’ showcase. Most Tevyes aren’t pure singers (recall Harvey Fierstein at the National Theatre only four years ago), and Hadary has no trouble making the reflective songs compelling.

Ann Arvia effortlessly gets the flinty warmth of Golde, Tevye’s wife, and the balanced cast is well anchored by the daughters (including Dorea Schmidt as Tzeitel and Maria Rizzo as Chava) and their beaux (Joshua Morgan as the skittish Motel, Kurt Boehm as a noble Fyedka). The frictions and bonds are palpable, and the subject seems evergreen as Tevye frets about changing traditions he is powerless to control.

Connoisseurs may hold out for the Broadway revival planned for next year to be directed by Bartlett Sher, so highly regarded with his velvet touch with the Lincoln Center’s “The Light in the Piazza” and “South Pacific.” That’s fine. Meantime, this “Fiddler,” keyed by Hadary’s wry and worried Tevye, is delightfully living up to this show’s durable traditions. Mazel tov, mazel tov.

Fiddler on the Roof

Book by Joseph Stein, music by Jerry Bock, lyrics by Sheldon Harnick. Directed by Molly Smith. Lights, Colin K. Bills; sound design, Lindsay Jones. With Valerie Leonard, Erick Devine, Joe Peck, Tracy Lynn Olivera, Alex Alferov, Jimmy Mavrikes, Kyle Schliefer, Curtis Schroeger, Trevor Illingworth and Thomas Adrian Simpson. Running time, about 2 hours and 40 minutes. Through Jan. 4 at Arena Stage, 1101 Sixth Ave. SW. Tickets $45-$119, subject to change. Call 202-488-3300 or visit www.arenastage.org.