“I’m a wet man,” Jonathan Groff announces early in “Just in Time,” a new musical in which he plays Bobby Darin. Mr. Groff, a Tony Award winner for his performance in last season’s gorgeous revival of “Merrily We Roll Along,” has not yet slipped into the role of the late singer, and he’s referring to his own reputation for prolific discharges of saliva while onstage.

Although this is something that is hardly uncommon among thespians, Mr. Groff acquired a particular notoriety a few years ago, after the blockbuster hit “Hamilton” was made available on DisneyPlus, showcasing the actor’s sendup of King George in a merciless closeup. This isn’t mentioned in the personal patter that begins the new show, but the star does quip, referencing three leggy ladies who will sing and dance alongside him, “Boy, are they gonna get spat on. And sweated on.”

It should be noted that more than a few women, and men, would welcome such an opportunity: Mr. Groff has been one of Broadway’s most reliably beguiling performers since playing a precocious teenager in “Spring Awakening” nearly two decades ago. In “Time,” the action unfolds on a main stage and in a smaller area directly across from it, and in between those spaces, where some audience members are also seated at tables, to create a nightclub-like atmosphere.

I sat at one of those tables during a recent preview and can report that I was neither spat nor sweated upon, though I was close enough to Mr. Groff and the other actors to notice that he does perspire a lot, at least here. That seems forgivable, as he’s required to be in almost constant motion — not only singing and dancing, but summoning the charisma and drive and anxiety of a consummate entertainer who knew he was living on borrowed time.

Darin, who died in 1973 at just 37, was a sickly child who wasn’t supposed to make it past adolescence, due to a failing heart. We’re reminded of this soon after Jonathan, as the star of “Time” initially introduces himself, becomes Bobby, and the restless ambition and tension that reportedly accompanied Darin’s rise to fame and rocky later career prove central to this musical — just as they were in 2004’s “Beyond the Sea,” a musical biopic starring Kevin Spacey.

The mawkishness that marred that film, which Mr. Spacey also directed and co-wrote, is generally avoided by director Alex Timbers, a master theatrical showman who also developed the stage musical, and librettists Warren Leight — whose credits range from the musical “Side Man” to “Law and Order: Special Victims Unit,” and whose father, his bio informs us, played trumpet for Darin — and Isaac Oliver. 

The actors occasionally spill into the aisles beyond the floor, reinforcing the sense that their characters are all there to engage and entertain us. Darin’s mother, or the woman he believes to be his mother — no spoilers for those who don’t know that part of his story — is played with great warmth and wit by a wonderful Michele Pawk, who captures the pluck and style of a woman who had been a performer herself. 

Gracie Lawrence is adorable as Darin’s early love, Connie Francis, though her rather shrill voice doesn’t evince the lush beauty of Ms. Francis’s singing. Erika Henningsen turns in a more textured performance, vocally and dramatically, in the meatier role of Darin’s wife of several years, Sandra Dee, whose devotion to him, at least as portrayed here, endured despite their conflicts and after their divorce.

Yet the show is Mr. Groff’s vehicle, and he rides it splendidly, and tirelessly. I’ll admit I was never a huge fan of Darin; notwithstanding his undeniable technical prowess, his delivery could, for me, have a smarmy, lounge-lizard quality. I’ve always preferred Louis Armstong’s take on “Mack the Knife,” and Frank Sinatra’s version of the title song of “Just in Time,” for that matter.

Yet in singing these tunes and others, Mr. Groff manages to channel Darin’s slickness with a rugged dynamism that lends a little more grit to the material, without ever losing sight of his subject’s eagerness to charm. The actor also charts Darin’s offstage life with sensitivity, from his troubled marriage and other personal and professional frustrations to the social consciousness he developed as Vietnam and the civil rights movement became pressing concerns.

As “Just in Time” tells it, though, Darin never felt more at home than he did in front of a crowd of adoring fans. And even if Mr. Groff lets us see him sweat, his bravura performance makes that abundantly clear.