Posted on February 8, 2015 at 6:02 pm

Wake up and smell the mai tais, New York. Las Vegas has come calling on you. And it’s on such good behavior, you’d be a churl not to embrace it as if it were a long-lost sibling.

As embodied by the bright and bouncy new musical “Honeymoon in Vegas,”which opened on Thursday night at the Nederlander Theater, the world capital of gambling and neon is everything you want it to be. That means a little hip, a little square, a little dangerous, a little kitschy and a whole lotta delicioussh fun. (Oh dear, am I slurring? Sorry.)

But here’s the bonus, in which East (Coast) meets West: This production is also a real-live, old-fashioned, deeply satisfying Broadway musical in a way few new shows are anymore. Adapted by Andrew Bergman from his 1992 movie, with a swinging score by Jason Robert Brown and a smooth-as-Ultrasuede star turn by Tony Danza, this show offers the perfect sunny holiday for frozen Eastern city dwellers.

But theater pundits have worried that the show might have lost its momentum in the meantime. An overextended preview period in the dead of a glacial winter and all but invisible advertising haven’t helped. Besides, musicals about Las Vegas have seldom worked on Broadway. (Even “Golden Rainbow,” a soft hit from 1968 starring Steve Lawrence and Eydie Gorme, was skewered as a paradigm of showbiz ineptitude in William Goldman’s Broadway bible “The Season.”)

So let’s pray that “Honeymoon in Vegas” doesn’t disappear before it finds its audience. Because what its creators have whipped up is an unlikely but scrumptious blend of cheese and caviar. And the career-high work here of Mr. Brown and Mr. Danza is so stealthily sophisticated that it takes you a while to realize the sly genius of what they’re doing.

The plot, which closely follows Mr. Bergman’s screenplay, is on one level rom-com formulaic. But it also detours, with extravagant swoops, into the realms of outlandishness and really good bad taste. The sweet nebbish Jack Singer (a likably exasperated Mr. McClure) wants nothing more than to marry his longtime, long-suffering girlfriend, Betsy Nolan (a charmingly self-deprecating Ms. O’Malley).

The problem is that Jack is paralyzed by the dying curse of his proprietary mother, Bea (Nancy Opel, hilarious), whose ghost keeps popping up to block his path down the aisle. So Jack and Betsy flee from New York to Las Vegas, where they encounter an equally formidable obstacle. That’s Tommy Korman (Mr. Danza), a big-time casino shark who instantly falls in love with Betsy, a ringer for Tommy’s late, lamented wife.

The course of true love runs on parallel roller-coaster tracks in “Honeymoon.” Tommy pursues Betsy with every clean and dirty trick at his disposal, and winds up winning the chance to spend a weekend with her after beating Jack, a born pigeon, in a poker game.

Poor Jack — portrayed by Mr. McClure with winning vestiges of the Everyclown-under-stress persona he perfected in the musical “Chaplin” — must overcome a mother’s curse, a powerful rival’s charm and his own wimpiness in an odyssey that takes him from Las Vegas to Hawaii and back.

That’s a lot of real estate to cover. But Anna Louizos’s perky sliding sets miraculously keep pace with the speeding story line, which winds up deploying singing ancestral Hawaiian statues and an airborne squad of Elvis impersonators. (Denis Jones’s choreography is functional, which under the circumstances is quite enough.)

As you may have inferred, “Honeymoon” doesn’t have a serious thought in its head. It is very serious, however, about creating a well-assembled entertainment in which every improbable element seems to spring from the same, dementedly logical sensibility. And that point of view is not one of snarky condescension toward the town of its title, but of amused professional respect.

You know this as soon as you hear the opening strains of the overture, one of the best in years. Mr. Brown, whose earlier and highly diverse work includes “Parade” and “The Bridges of Madison County,” here finds a shiny, fertile common ground between brassiness according to Broadway and to Las Vegas.

His songs seamlessly propel plot and define character in the way numbers did in the heyday of Rodgers and Hammerstein. But he often inflects them with the ring-a-ding swell and swing you associate with Frank Sinatra recordings from the late 1950s and early ’60s.

He’s not just quoting or sending up that style; he’s embracing it on his own terms as a keen-eared fan of today. And in a breakout performance, Mr. Danza (still best known for the television sitcoms “Taxi” and “Who’s the Boss?”) matches the nuanced flash of the music.

His Tommy is an ever-mellow figure of both menace and romance, a criminal pragmatist with a soft, dreamy side. He speaks in a foggy near-monotone, with an impeccably shaved poker face to match.

But what he conveys with the tiniest inflection or quirk of a finger is immense, and the sum effect is a fabulously sober comic portrait. When he sings, in the show’s most irresistible ballads, he sustains the same sense of hot-and-cold steel wrapped in velvet. Tommy regularly occupies the Frank Sinatra Suite at the Milano Hotel, where much of the action is set, and as Mr. Danza plays him, he belongs there.

My favorite song of Tommy’s is “Out of the Sun,” an account of how his wife, Donna, a sun worshiper, died of skin cancer, which has all the cool wistfulness of Sinatra doing “It Was a Very Good Year.” Just listen to the melancholy resonance Mr. Danza lends the word “saddlebags,” which is how the doctors described Donna’s skin at the end.

The tightrope between high wit and low humor is walked most adroitly by a supporting cast that includes Catherine Ricafort as a Hawaiian Mata Hari in Tommy’s employ; Matthew Saldivar as Tommy’s sidekick, Johnny Sandwich (he changed his last name from Foccacia); and, best of all, David Josefsberg as both the unctuous M.C. of a hotel floor show and a deus ex machina of an Elvis impersonator.

Mr. Josefsberg nails both types with a precision that stops short of out-and-out parody. It may sound odd to praise a show as willfully silly and energetic as “Honeymoon in Vegas” for its restraint.

But there’s an unswerving professionalism at work here that consistently turns excess into something sharp, sweet and surprisingly refined. Tommy might use a cruder metaphor for this alchemical process — maybe something ending with “shinola” — but he’d say it like the unimpeachable gentleman gangster he is.