Like people, plays or films can sometimes show more substance than they suggest on a first impression. Take Broadway’s newest comedy, “The Cottage,” which focuses on a string of adulterous affairs disclosed on an early summer day in 1923, in the English countryside.

To be more specific, the action unfolds in the kind of sprawling manor, splendidly evoked by Paul Tate dePoo III’s lushly appointed set, that only the most privileged of Brits would describe as a cottage. Playwright Sandy Rustin, best known for her stage adaptation of the film “Clue,” has six characters pass through who end up composing more than three couples. We first meet lovers Sylvia and Beau; each is married to someone else, and each suggests a slightly hysterical escapee from a Noel Coward parody.

Sylvia and Beau are respectively played by a musical theater veteran, Laura Bell Bundy, and a “Will & Grace” star, Eric McCormack, himself an accomplished trouper, and both are infectiously game and often very funny, as are their fellow actors, who play similarly ridiculous types. Still, by the time intermission arrived at a recent matinee, I’ll admit I was thinking longingly of the summer day that awaited outside the theater, where the weather had dropped to a brisk 80 degrees after a heat wave.

Duty bound me to stick around, of course, and I’m glad I did. Because while “Cottage” could have worked well enough as a one-act lark, its second act offered both richer comedic nuggets and an unexpected payoff. It turns out that, in Sylvia, Ms. Rustin has crafted an appealing feminist heroine — not in the self-conscious sense that the term can bring to mind nowadays, but more in the mold of old-school dynamos who delighted movie audiences with their mettle and wit in the decades after “Cottage” is set.

Under the impish direction of a “Seinfeld” alumnus, Jason Alexander, Ms. Bundy, whose most high-profile stage roles to date have been sassy ingénues, emerges as this kind of figure gradually. The actress is first seen fluttering around in frilly white lingerie — Sydney Maresca’s period costumes are as scrumptious as the scenery — while Sylvia waits for Mr. McCormack’s delightfully smug Beau to emerge from the shower.

But Beau’s “Tulip,” as he calls Sylvia, will soon be brought crashing down to earth by a string of betrayals and revelations, and while her initial response is to fret and fuss, she eventually proves to be made of sharper, sturdier stuff. Ms. Bundy traces this evolution with poise and pitch-perfect comic timing, in a performance that nods cleverly to her star turn as Elle Woods in “Legally Blonde” — another character whose superficial frivolity led others to underestimate her — while demonstrating a clear capacity for more mature roles.    

The other players are just as facile in fielding Ms. Rustin’s script, which features farcical and scatological elements. One of the funniest sequences involves Beau’s heavily pregnant wife, Marjorie, played by a wonderfully deadpan Lilli Cooper, and features no dialogue, so that the only sounds to be heard at the preview I attended were the audience’s cackles of laughter.

As Sylvia’s cloddish husband, Clarke, Alex Moffat, who has gained attention in recent years for his impersonations of political and media figures on “Saturday Night Live,” proves especially adept at the physical comedy that becomes prominent in the staging. Nehal Joshi and Dana Steingold ably round out the cast as, respectively, a mysterious intruder and a daffy coquette with secrets of her own.

Notwithstanding Sylvia’s arc, you won’t leave “The Cottage” feeling challenged or enlightened, but that’s plainly not its larger purpose. Ms. Rustin and Mr. Alexander and his company have given us a tonic, full of blithe spirit, and in this summer of our discontent, it’s a welcome distraction.