‘Kimberly Akimbo’ is on Broadway, and the world is better for it.

At the musical’s center is an entrancing performance by Victoria Clark that may have audiences inquiring after the show — which had its official Broadway opening Thursday night at the Booth Theatre — about adopting her. Okay, as she is 63, that would probably be frowned upon. But in the two-act musical by David Lindsay-Abaire and Jeanine Tesori, Clark plays a 15-year-old so convincingly that it wouldn’t be surprising if the younger cast members didn’t pick up a pointer or two about portraying people their own age.

That is not to diminish the special accomplishments of everyone in this exemplary cast of nine, unfolding the story of a New Jersey teenager named Kimberly who is aging at “four or five times” the normal rate because of a rare genetic disease. The conceit — based on Lindsay-Abaire’s 2000 play of the same title — keeps us toggling all evening between laughter and tears, as Kimberly is compelled to deal with the complicated issues of growing up, and growing old. All at the same time.

The actors return to the roles they originated last year at off-Broadway’s Atlantic Theater, in a production directed by Jessica Stone that seems even more assured, and lyrically tighter. Justin Cooley, playing sweet-natured Seth, a high school nerd whose extracurricular flex is anagrams, makes a smashing Broadway debut as a kid who sees Kimberly’s spirit rather than her wrinkles. Alli Mauzey and Steven Boyer excel as Pattie and Buddy, the immature parents who don’t know how to love Kimberly. Above and beyond is Bonnie Milligan, portraying Pattie’s larcenous sister Debra, a woman of no known address but who might be elected president if she could redirect that cyclonic energy away from antisocial impulses.

Lindsay-Abaire and Tesori situate “Kimberly Akimbo” in the northern New Jersey suburbs of Bergen County, where everything is supposed to hew toward middle-of-the-road serenity but is, in fact, a hotbed of dysfunction. “Akimbo,” with its connotation of haphazardness, could be the nickname that Buddy and Pattie give their home: For all intents, they and Debra are children and Kimberly the besieged adult, enduring their whining and trying to talk them out of their bad ideas.

Don’t let the story’s modest narrative boundaries give you the impression it’s not Broadway-boffo. Not every musical needs a chorus. Well, actually, this one has one an endearing mini-version, via the performances of Olivia Elease Hardy, Fernell Hogan, Nina White and Michael Iskander, as Seth and Kimberly’s romantically confused classmates. Thankfully, they are not up-talking, eye-rolling caricatures; they’re likable kids gradually passing through one emotional phase after another — with recognizably adolescent eruptions of insecurity, selfishness, terror and sweetness.

Clark’s Kimberly is in point of fact epic, a profile in courage, a heroic display of grace under potentially the most embittering circumstances. She doesn’t have what comes across in “Kimberly Akimbo” as an absolute luxury: time. (People with her condition, she reports, live on average only to age 16.) You may experience Kimberly’s story as a brave affirmation of the recommendation artists have been urging for centuries: to really, fully live, right now. “Getting older is my affliction,” Kimberly sings to her classmates. “Getting older is your cure.”

Lindsay-Abaire’s book and lyrics and Tesori’s music take their cue from the Kimberly they dream up: Kimberly tries her darnedest not to feel sorry for herself, and the authors pay her the respect of not permitting us to sentimentalize her much, either. (Her aging malady is never given a name, not even in the very funny classroom scene in Act 2, when the students pair up in class to sing their reports on the diseases they’ve chosen to study.)

The score exudes observational-comedy sharpness — the sort that recalls the craftsmanship of songwriting finely tailored to the contours of character and motivation. “Hello, Darling,” the lullabye sung by Mauzey’s pregnant Pattie and reprised by Boyer’s Buddy, works both as a funny commentary on expecting a child and Pattie and Buddy’s cluelessness: The melody may be pitched in the key of nurturing, but the words make clear that this chronically unhappy couple is incapable of protecting the beings they bring into the world from their petty grievances and anxieties.

Then there’s the Act 2 opener, “How to Wash a Check,” one of the delirious numbers bestowed upon Milligan’s Debra, who, in the basement of Pattie and Buddy’s home, offers Kimberly and her impressionable pals a primer on the forgery scheme she’s sucked them all into. (Don’t try writing a scene like this at home; wringing the setup for laughs is musical comedy composition of a high order.)

High school life in the ’burbs is conjured resonantly by set designer David Zinn, in scenes of beanbag chairs in the school library and ice skaters gliding across the local rink where Seth works and makes announcements on a badly amplified P.A. system. Costume designer Sarah Laux aptly dresses everyone as if she’d shopped for them at the mall in Hackensack, with extra loving attention devoted to Kimberly’s get-ups, jumpers with embroidered flowers and the like.

The costumes certainly aid in the illusion that Clark is a teenager, though she doesn’t seem to need much help. The release from the strictures of time and age is remarkable in the portrayal: It conveys a mysterious mixture of innocence and wisdom, of both youthful brashness and mature vision. It’s difficult at times to reconcile this Victoria Clark with the Victoria Clark who 17 years ago won a Tony as the demure mother of a mentally disabled daughter in Adam Guettel’s lyrical “The Light in the Piazza.”

Ah, right — acting! You won’t find anything akimbo with this Kimberly. Or askew in this lovely, embraceable show.

Kimberly Akimbo, book and lyrics by David Lindsay-Abaire, music by Jeanine Tesori. Directed by Jessica Stone. Choreography, Danny Mefford; music direction, Chris Fenwick; sets, David Zinn; costumes, Sarah Laux; lighting, Jeanette Oi-Suk Yew; sound, Kai Harada; orchestrations, John Clancy. About 2½ hours. At Booth Theatre, 222 W. 45th St., New York. telecharge.com.