Bernadette Peters in “Hello, Dolly!” (Julieta Cervantes)

NEW YORK — After the tornado, the rainbow.

If Bette Midler’s Dolly Gallagher Levi was a dizzying whirlwind of bite and bluster, Bernadette Peters’s is a gentler event, one of endearingly zany charms and touching warmth. She’s the polish on Midler’s brass.

And as the new crooning busybody of director Jerry Zaks’s bubbly revival of “Hello, Dolly!” — a show-tune machine that now purrs like an impeccably maintained Cadillac — she arrives at the Shubert Theatre to spread further the old-school joys of songwriter Jerry Herman and book writer Michael Stewart’s handiwork. Indeed, Peters-as-Dolly feels like the keeping of one of Broadway’s sacred promises. For a certain caliber of musical theater star, Dolly is a rightful inheritance, an essential turn in the spotlight predestined over the years for the likes of Carol Channing and Pearl Bailey and Mary Martin and Ethel Merman and now, for Midler and Donna Murphy and Peters and Betty Buckley (who’ll play her in the national tour).

That splendid Herman lyric, “ … so nice to have you back where you belong … ” raises fresh lumps in the throat each time one of these great dames descends that Harmonia Gardens staircase. And of course, they’re raised again when Peters materializes at the top of the stairs in that smashing red gown and crown of red feathers by Santo Loquasto. (Where, by the way, does Dolly get these amazing dresses?)

In any event, at the top is exactly where Peters belongs.

In tandem, too, with the indispensable Victor Garber, who takes over the role of Dolly marriage target and comic foil Horace Vandergelder from David Hyde Pierce, Peters’s performance propels the character in a more adorable, embraceable direction. Midler was outrageously clownish and her Dolly an expression of independence and flamboyant impulse. After each of the confidences she shares with her beloved dead husband, Ephraim, about her plan to hook Vandergelder, you could easily have imagined Midler’s Dolly turning to the orchestra and bellowing: “Horace, Schmorace. Maestro, give me a C!”

Victor Garber and the ensemble of “Hello, Dolly!” (Julieta Cervantes)

With Peters, Dolly’s melodically wistful musings about not wanting the parade to pass her by — did any parade ever dare pass Midler by? — are more heartfelt. And her conversations with her late husband seem to emanate from a more poignant place; she really does seem to be pouring out her soul to him, and to us.

The thoroughly winning Garber, who embodies Horace here not so much as the requisite tiresome grouch but as a big, entitled kid, asserts his own comic energy; it’s the loosest I’ve ever seen him on a stage, and the funniest. That buoyancy extends to Kate Baldwin, whose Irene Molloy comes across now as more youthful and mischievous. Other newcomers to the cast include, spectacularly, the emerging musical star from London, Charlie Stemp as Barnaby, and a delightful Molly Griggs as Minnie Fay. Christian Dante White, filling in for an ailing Gavin Creel, makes for a gorgeously sung Cornelius. Keep an eye out for this magnetic actor. You’ll be seeing him somewhere soon executing a big turn all his own.

Bernadette Peters in “Hello, Dolly!” (Julieta Cervantes)

Peters’s voice shows a few telltale signs of wear and tear, but otherwise, this actress seems to possess the power to make time stand still. Which is only apt for a musical that visits us from another time, and still exudes such a gleeful capacity for stowing away the worries of the world, for a few happy hours.

Hello, Dolly! music and lyrics by Jerry Herman; book by Michael Stewart. Directed by Jerry Zaks. Choreography, Warren Carlyle; sets and costumes, Santo Loquasto; lighting, Natasha Katz; music direction, Andy Einhorn; sound, Scott Lehrer; orchestrations, Larry Hochman. With Will Burton, Melanie Moore, Jennifer Simard, Kevin Ligon. About 2 hours 40 minutes. Tickets, $39-$149. At Shubert Theatre, 225 W. 44th St., New York. Visit or call 212-239-6200.