Depending on your reading habits and areas of interest, you likely know Anthony Rapp primarily as either one of the original stars of the Pulitzer Prize-winning hit musical “Rent” and its screen adaptation, or as the guy who accused Kevin Spacey of making sexual advances toward him when Mr. Rapp was 14, setting in motion the chain of events that would essentially end the older actor’s career in disgrace.

If the latter is your answer, “Anthony Rapp’s Without You,” the new autobiographical, one-man (plus band) show that Mr. Rapp wrote and is now performing, may not be of great interest. In fact, if you’re not a fan of “Rent” — or if, like me, you think Jonathan Larson’s lavishly celebrated 1996 rock opera is charming and poignant but overrated — this 90-minute piece might, on its face, seem to hold limited appeal.

Pairing Mr. Rapp’s conversational libretto, based on a memoir of the same name, with music by Larson — and additional songs written by Mr. Rapp and a few collaborators — “Without You” focuses on the handful of years during which both men rose to fame. It’s also, as the title suggests, an account of loss, tracing both Larson’s untimely death at 35, on the day before “Rent” had its first preview performance off-Broadway, and the passing of Mr. Rapp’s mother, after a prolonged battle with cancer. 

The latter, whom Mr. Rapp refers to as Momma, worked as a nurse while raising him and his two siblings at Joliet, Illinois; she continued working after starting chemotherapy, he informs us, and never complained, even after the illness forced her to quit and left her in constant pain. The eldest of 13 children, she “could name all of her brothers and sisters in a single breath,” and supported Mr. Rapp’s ambitions unequivocally. Despite struggling to come to terms with his homosexuality, she eventually resolved, “It’s no different from having blue eyes or brown eyes, really.”

Mr. Rapp’s portrait of Larson — who gained some more posthumous attention a couple of years ago, when Andrew Garfield played him in a screen adaptation of the late artist’s “tick, tick…BOOM” — is equally reverential, if somewhat less idealized. Mr. Rapp describes the composer and playwright who would change his life, at their first meeting, as “a young, curly haired guy, with ears that stuck out a bit.” He later remembers Larson introducing himself to a stranger as “the future of musical theater.”

Granted, Mr. Rapp doesn’t contest this boast. While revisiting the rehearsal process that carried “Rent” from its promising workshop to downtown success and then a triumphant Broadway run, he delivers Larson’s songs — and reprises them, on more than one occasion — with an almost evangelical zeal. Recalling the company’s first run-through of “Seasons of Love,” which also opens and closes “Without You,” Mr. Rapp gushes, “I had never heard a song like it.” 

The audience at the preview I attended certainly returned his fervor. The five musicians who accompany Mr. Rapp onstage — a keyboardist, guitarist, bassist, cellist, and drummer — provide supple, graceful support throughout the show, even in those moments when the star and writer’s tributes and confessions threaten to become treacly.

At a time when snark and solipsism have become ever-growing sources of creative inspiration, it’s striking — and refreshing — that Mr. Rapp would make this deeply personal work an homage to two people who had such abiding and positive influences on his life.

I still highly doubt that, had Larson not died tragically, he would have become the Stephen Sondheim of his generation. Yet the affection that fuels “Without You” — for both him and Mr. Rapp’s mother — is infectious, and it ultimately transcends, or at least mitigates, the show’s flashes of banality.