NEW YORK — That director Bartlett Sher should be considered a master of the Golden Age musical is reaffirmed with his latest handiwork, the deeply affecting revival of “Fiddler on the Roof” that had its official opening Sunday night at the Broadway Theatre. In the wake of his exquisite treatments of Rodgers and Hammerstein’s “South Pacific” and the still-running “The King and I” at Lincoln Center Theater, Sher reveals an equally perceptive eye and ear for Joseph Stein, Jerry Bock and Sheldon Harnick’s 1964 melody-rich account of the persistent hardships and simple joys of life in a besieged Jewish shtetl.

He’s done himself — and audiences — a huge favor with his astute casting, particularly in the choice of Danny Burstein in the all-important role of Tevye, the impoverished milkman who is forced to come to terms with a changing world by his restless daughters. Burstein, seen at the Kennedy Center as an aptly forlorn Buddy in the 2011 revival of “Follies,” brings a becoming warmth to his Tevye, in a performance that never tips over into showiness: this is a man who seems authentically wrenched by the position he’s in, torn between the ways he knows and the children he wants to make happy. It’s a wryly, fully realized portrayal, one that gathers strength as the weight of outside events bears down on his little, out-of-the-way village of Anatevka, in Czarist Russia.

A most advantageous match has been made for this Tevye, in the terrific Jessica Hecht as his long-suffering wife Golde; her take-no-guff tartness allows the bickering between them to sound as if it is the reassuring background noise of a long, unspoken affection. Indeed, their push-me-pull-you chemistry is a splendid set-up for their tender Act 2 ballad, “Do You Love Me?”, in which Tevye and Golde grudgingly have to admit — without getting meshugge about it, mind you — that yes, being together hasn’t been so bad. And around this central pair orbit other excellent actors, among them, Alexandra Silber, Samantha Massell and Melanie Moore as the “Matchmaker, Matchmaker”-singing oldest daughters; Adam Kantor, Ben Rappaport and Nick Rehberger as their various suitors and Alix Korey, playing a businesslike busybody of a Yenta.

“Fiddler” has been belittled in some quarters over the years as a schmaltzy relic. It’s nothing of the sort. It endures, in point of fact, as a meticulously well-built musical, a bit overlong, maybe, but with a whole raft of smashing numbers, from the exhilarating opening song, “Tradition,” all the way through to the plaintive closing refrains of the finale, “Anatevka.” Sher’s production underlines the inherent strengths and adds to them, with some thrilling dances, choreographed by Hofesh Schechter (and inspired by the steps in director-choreographer Jerome Robbins’s original version), and a beautiful physical production by set designer Michael Yeargan. The wooden-house set pieces and multi-hued backdrops that fly gracefully in and out betoken the humble, homespun lives outlined in the stories of Sholom Aleichem, on which the musical is based.

Sher has come up with his own original prologue and epilogue for the evening that are meant to plant a connection between the flight out of Anatevka of the village’s Jews, forced to flee by the Czar’s soldiers, with the current refugee crises around the world. We first see Burstein in a modern overcoat, gazing up at a signpost for Anatevka. He reads Tevye’s first lines of the musical from a book, and removes the coat to reveal Tevye’s costume, for “Tradition.” At evening’s end he’s seen again in his overcoat, joining the populace streaming out of the village, on a march to wherever is next. The intent behind the gesture is hard to quarrel with, even if the concept itself is already implicit in the musical. It doesn’t take an actor in contemporary dress for “Fiddler” to stir the contemporary conscience.

In any case, the lovely contributions all around assure that “Fiddler” has earned its return visit to Broadway, and even helps to erase the memory of some inferior incarnations of the recent past. And in Burstein’s Tevye, we get the surest sign yet of this put-upon dairyman as a devoted father. You feel that Tevye’s love for his children is as certain as every sunrise, and sunset.

Fiddler on the Roof, book by Joseph Stein, music by Jerry Bock, lyrics by Sheldon Harnick. Directed by Bartlett Sher. Choreography, Hofesh Schechter; music direction and orchestrations, Ted Sperling; sets, Michael Yearn; costumes, Catherine Zuber; lighting, Donald Holder, sound, Scott Lehrer. With Nick Rehberger, Ben Rappaport, Jenny Rose Baker, Hayley Feinstein, Alix Korey, Adam Grupper, Adam Dannheisser. About 2 hours 50 minutes. Tickets, $35-$227. At Broadway Theatre, 1681 Broadway, New York. Visit telecharge.com or call 212-239-6200.