Princess Theatre musicals. Ever heard of them? If so, I have got the show for you. If not … I have got what could well be the show for you, too. “The Drowsy Chaperone” is the name of both this inspired bit of nostalgia and the onstage early-20th-century trifle to which it pays lavish, loving tribute. With a marvelous actor named Bob Martin serving as tour guide through both incarnations, “Drowsy” will offer hard-core musical theater buffs a buoyant trip down a faux memory lane. Everyone else will get a fizzy, smart, and very funny look at how even what seem like the most disposable bits of pop culture can take root in one’s unsuspecting head and heart.

Historians like to talk about how first “Show Boat” and then “Oklahoma!” revolutionized musical theater, and they’re right. But many of the predecessors to these shows were also delightful. And many of them debuted at the tiny Princess Theatre on West 39th Street. Before writing “Show Boat,” Jerome Kern teamed up with Guy Bolton and eventually P.G. Wodehouse in the 1910s to write a series of well-crafted miniatures for the Princess like “Very Good Eddie” and “Oh, Boy!”

These musicals were pioneering in their use of (relatively) interesting songs to propel (relatively) plausible characters. To today’s audiences, they’re fairly creaky, with their vaudeville vignettes and tidy resolutions. But as anyone who’s ever found himself captivated by Turner Classic Movies at 1:30 in the morning can attest, those creaks can have a music all their own.

Which brings us to “The Drowsy Chaperone” – the fake one, allegedly written in 1928, the one that our bashful narrator puts on his record player one day when he’s feeling blue. He freely admits that it’s a two-dimensional lark about gangsters and showgirls and multiple weddings, and yet the Man in the Chair becomes giddy at nothing more than the static on the record before the overture begins. “I love that sound,” he says. “To me, it’s the sound of a time machine starting up.”

In no time at all, the Marquis Theatre becomes just that, as Casey Nicholaw (making a remarkably assured Broadway debut as director) morphs David Gallo’s seemingly banal apartment set into a roaring ’20s tableau and “The Drowsy Chaperone” begins. From the daffy opening number to the high-flying finale, the Man in the Chair patiently explains, apologizes for, annotates, and mostly basks in the hokey joys of his beloved “Chaperone.” (The title refers to the leading lady’s minder, whose penchant for champagne renders her less than vigilant.)

At the onset of one typical scene, the boy’s blindfolded and on roller skates, the girl’s affecting a French accent, they sing a duet, and the Man in the Chair blurts out, “This scene couldn’t be more ridiculous!” He’s right, but his unwavering affection proves surprisingly infectious. This carries through to the effervescent period score by composer-lyricists Lisa Lambert and Greg Morrison; replicating the Kern-Gershwin-Porter era of songwriting isn’t easy,but they manage the trick nicely. (Don McKellar and Mr. Martin himself wrote both the Man in the Chair’s narration and the script for the play within the play.)

As painfully and lovingly aware as the Man in the Chair is of the musical’s flaws, though, this daffy old bit of froth is always allowed to speak for itself. No matter how many times the record is interrupted or how ridiculous the dialogue gets – “Why are we dancing? Our dreams are in tatters” – the “Drowsy” actors perform with absolute honesty. There are no campy double takes, no eye-rolling apologies for the material, no fourth-wall-dissolving tricks at all.

It helps that Mr. Nicholaw and his writing team have immersed themselves in the period, with its extraneous vaudeville shtick and fearless layering of subplots and sub-subplots. Mr. Nicholaw also choreographed the show, and jazzy numbers like “Toledo Surprise” and “Cold Feets” stop the show in all the right ways. (Special credit to Larry Blank, Glen Kelly, and Phil Reno for their flawless orchestrations and arrangements.)

Perhaps the most awkward discrepancy is that of scope. The Princess Theatre seated 299. These days, you’re most likely to see a show of this (purported) vintage at Connecticut’s similar-size Goodspeed Opera House. The Marquis has more than 1,600 seats, and the intimate pleasures of nonsense like “Drowsy” – already a tough sell in today’s climate – are hardly shown to their best advantage in a theater that large.

But Mr. Nicholaw’s powerhouse cast does everything it can to overcome this hurdle. Eddie Korbich, the most reliably superb character actor in musicals today, lives up to his impeccable standards as the anxious best man, while Edward Hibbert’s unflappable butler, Beth Leavel’s bibulous title character, and Danny Burstein’s uproarious Latin lover (“a man of a thousand accents,” the Man in the Chair explains, “all of them insulting”) lend stellar support. Sutton Foster isn’t asked to do much she hasn’t done before as the ingenue, but she brings consummate pizzazz and skill; she is paired with Troy Britton Johnson as the plausibly ludicrous leading man.

And every musical should have an advocate as engaging as the wonderful Mr. Martin, whose expository notes gradually slip into a deeply personal confession of why the show means so much to him. As its charms become more personal to the Man in the Chair, they paradoxically grow more accessible to us. By the end, the real world may have once again intruded on his solitude, but Mr. Nicholaw and the writers have found a way to turn a seemingly extraneous “Drowsy” ballad into something close to an epiphany. The scene couldn’t be more ridiculous. And it’s hard to imagine it – or the rest of “The Drowsy Chaperone” – being more inviting, tuneful, or more magical.

Open run (1535 Broadway at 46th Street, 212-307-4100).