As soon as the curtain rises to reveal a line of men dressed in pale-blue uniforms and carrying instrument cases in what appears to be an Israeli bus station, you know you are in good hands.

The men seem just a bit wary, a little discomfited to be where they are. Their uniforms look fairytale resplendent compared to the grubby green of the Israeli soldiers, and their manners charmingly old-fashioned next to the standard Israeli gruffness. But it’s when one of the men confuses Petah Tikvah, where they have been invited to perform at the opening of an Arab cultural center, with Bet Hatikvah, a godforsaken speck of a town in the periphery, that “The Band’s Visit” really takes off.

The rest of the 90-minute show is a sweet and sad examination of the sorrows and regrets as well as the promise and possibility in every life, and it is punctuated with wonderful songs and pitch-perfect performances.

Adapted by Itamar Moses from the 2007 Israeli film of the same name, the show sticks pretty close to the original plot. When the Alexandria Ceremonial Police Orchestra get on the wrong bus and ends up in the middle of the Negev, the musicians try to explain that they are scheduled to perform at the new Arab cultural center. “There is no Arab cultural center,” the cafe owner Dina explains. “There is no culture here at all.” Since there are no more buses out of town, Dina invites the men to spend the day and night with her and some other townspeople. They can leave in the morning for Petach Tikvah.

Rather than feeling suspicious and frightened at the arrival of a group of unknown Arabs, the townspeople of Bet Hatikvah seem delighted that something different has finally happened. There actually are new people to talk with.

The orchestra’s leader, Tawfik, reluctantly agrees, and he and the flirtatious trumpeter, Haled, go with Dina. The clarinetist, Simon, who has written a few bars of an unfinished concerto, joins an unhappy young couple, Itzik and Iris, who live with her father, Avrum, and their baby. Itzik has been out of work for some time, and as soulfully played by John Cariani, he feels both stuck and at loose ends, while his wife is resentful and frustrated that she has to take care of “two children.”

In a fantastic performance, Katrina Lenk embodies Dina, a lonely, disappointed woman who still has the capacity to yearn for something more. In the best number in the show, “Omar Sharif,” she recalls how, when she was young, she and her mother listened to the famous singer Umm Kulthum on Egyptian radio and watched Omar Sharif in Egyptian movies, thrilling to the romance and mystery. “A jasmine wind from the west and the south/ honey in my ear, spice in my mouth,” Lenk sings. Lenk was terrific in “Indecent,” the recent show about a scandalous Yiddish play, and she is even better here. Exuding sensuality and a time-roughened sensitivity, she partners perfectly with Tony Shalhoub as Tawfik. He is as reserved and repressed as she is needy of affection and stimulation.

Scott Pask’s ingenious set design symbolizes the play’s themes of attempted and missed connections. As the rotating stage moves, the actors step on and off, moving forward and backward. The shabby tables outside of Dina’s, the modest dining room at Itzik’s, all capture the essence of Bet Hatikvah, a town that the government plopped in the middle of nowhere. In its simplicity, the set avoids swamping the delicate story, and that’s something to be grateful for.

Dina describes her hometown, “Stick a pin in a map of the desert./Build a road in the middle of the desert./Pour cement on the spot in the desert.” The lyricist/composer of “Dirty Rotten Scoundrels” and “The Full Monty,” David Yazbek has written lyrics that are consistently clever and often very moving, and his music beautifully combines Middle Eastern rhythms with classic musical-theater ballads. The songs definitely move the action or reveal character, as musical theater songs need to do. Director David Cromer keeps the whole show moving forward seamlessly. It’s an exceptionally successful collaboration that makes for a wonderful show.