Claire is low on energy, so she pops across the hall to Oliver’s pad for a pick-me-up. But Oliver, a creature of routine, doesn’t like being interrupted while listening to jazz and waiting for mail. She insists, he gives in, and a spark, maybe a literal one, is ignited.

Never was a meet cute as cute — and as quietly ominous — as it is in the musical “Maybe Happy Ending,” which opened Tuesday at the Belasco Theater. That’s because the pair are robots, and Claire’s battery is running down fast. Hooking her up to his charger may signal, for Oliver, the beginning of love. It may also signal the end of it.

That we nonrobots also connect, pair and empower one another to share a too-brief lifetime is the surprising double vision that makes “Maybe Happy Ending” a ravishing addition to the catalog of Broadway nerdicals. The term is high praise, honoring supersmart, usually small-scale shows — like “Fun Home,” “The Band’s Visit” and “Kimberly Akimbo” — that nevertheless have big emotional impact. This one, directed with breathtaking bravura by Michael Arden, gets bonus points for difficulty, too: Under cover of sci-fi whimsy, it sneaks in a totally original human heartbreaker.

The sci-fi elements are handled lightly and humorously in the book by Hue Park and Will Aronson, thus dodging the invidious scrutiny that the genre often elicits. By 2064, when their story takes place, Helperbots — android servants like embodied Siris — have been assisting humans with daily tasks for decades. But Oliver (Darren Criss) and Claire (Helen J Shen) are now obsolete, living out their days in a pleasant retirement home in Seoul as their operating systems antiquate and replacement parts become scarce.

Still, they remain fully sentient and distinct. Oliver, an early model Helperbot 3, is more stylized and herky-jerky than Claire, a later model Helperbot 5. His lips are pursed, his feet splayed, his language not quite natural (he can’t stop saying “thank you”) and his hair a hard helmet like a Playmobil figurine’s. Even so, he spent enough years with his former owner, James Choi, to have absorbed some human analog tastes — the jazz LPs especially — and to miss him fiercely. Surely Choi (Marcus Choi, excellent) will reclaim him one day.

Claire is smoother, nearly convincingly human, in full command of snarky eye rolls and chic in a pleated gold skirt. (The just-weird-enough costumes are by Clint Ramos.) Claire is also wiser than Oliver and, perhaps inevitably, less durable as a result. Having seen how humans discard one another — her memories of the unhappy couple that owned her are screened for us like a Neorealist film — she knows that Choi is never coming no matter how long Oliver waits for the mail. And yet her greater facility with emotion prompts her to protect him from that awful knowledge.

None of this is mawkish; robots do not have funks. Nor are the songs, with music by Aronson and lyrics by him and Park, the usual bombastic ballads one hears in Broadway love stories. Oliver and Claire get mostly upbeat, busy numbers, stylistically landing somewhere between Bacharach and Sondheim. That’s a very nice place to land.

Not that deeper emotion is avoided. In a clever touch that becomes much more, Choi’s (and thus Oliver’s) favorite jazz singer, a Sinatra-like crooner named Gil Brentley, pops up periodically to offer I’ve-been-there commentary in midcentury — 20th century — mode. In particular, Brentley (Dez Duron) starts and ends the show, accompanied by Aronson’s lush, string-heavy orchestrations, with the heartbreak song “Why Love,” offered first in regret and then in recommendation.

In between, we see Oliver and even the more cynical Claire make the same journey. For them, though, the journey is also literal, as Oliver decides to search for his owner and Claire decides she has no choice but to accompany him. (Being a Helperbot 5 means she knows how to drive.) A classic robot road trip ensues, with the two growing closer as they share adventures involving a ferry ride to an outlying Korean island, an overnight stay at a Motel Sexx and an enchanted evening of fireflies in the forest.

But no more of the plot. It’s too subtle for summary anyway, and worth coming to cold.

I didn’t quite: I happened to be in Atlanta in 2020 when “Maybe Happy Ending” was staged by the Alliance Theater there (after earlier productions in South Korea). Fine as it already was, the show feels new and more overwhelming on Broadway, the consequence of a staging so fully imagined, sensitively expanded and brilliantly executed that it’s impossible to tell where one element ends and another begins. The dazzling iris effects of Dane Laffrey’s sliding-panel set and the saturated colors of Ben Stanton’s lighting merge with video elements (by Laffrey and George Reeve) that are among the most sophisticated I’ve seen. (Yes, there are holograms.) Peter Hylenski’s subtle sound design makes you feel as if you are in the characters’ world, not their lungs.

That combination of abandon and restraint means you are never clobbered or cloyed by the gorgeous effects the way you are (to choose randomly) in “Sunset Boulevard.” The same applies to the acting, which is daring enough to tell the robot story yet not so extreme as to obscure the human one. Criss, who has sometimes seemed stiff onstage, is especially fine here, delivering a startlingly gestural performance, all tics and glitches, that never obscures the true feeling within. The trap of twee is thus thoroughly avoided. And Shen, making a confident Broadway debut, similarly backfills Claire’s facade of wit and smart-girl impatience with the surprise and pain of newfound affection.

Though she also sings, as Criss does, divinely, their singing is never an end in itself; it is how we feel that their story is ours. And when their duets become trios with Duron’s Gil Brentley, we understand just how powerful popular music can be: It has given these robots hearts.

What “Maybe Happy Ending” asks, even in its ambivalent title, is whether that’s a good thing, for them and for us, their mirror images. When Oliver fully realizes that Claire’s “shelf life” will end before his, he asks in real pain, “How can people do this?” — meaning survive the death of others. If the start of love is the start of loss, is it perhaps better to erase one’s memories (which these Helperbots can do because they have their own passwords) or even to avoid the journey altogether?

A good question for robots and, as posed by this astonishing musical, maybe the most deeply human one of all.