Patina Miller could do no wrong Friday night at the Kennedy Center’s Terrace Theater, even when things weren’t quite going right. The Tony-winning star of Broadway’s current “Pippin” nearly forgot to introduce the quartet playing with her, despite broad hints from pianist and music director James Sampliner. And during an unplanned extra encore, she fumbled the lyrics of “New York, New York” so thoroughly that she had to reboot.

No matter. The crowd roared with approval as soon as Miller safely cleared the first verse.

This Barbara Cook Spotlight Series is in its seventh year of showcasing Broadway singers, but it’s never seen a love fest like this. You could see the appeal: Miller’s not a devastating vocalist, but she’s a very good one, as she proved immediately by accelerating through styles and gears for the Kander and Ebb anthem “Sing Happy.” She moves beautifully — the lithe young Miller first came into view as part of the Tribe in the 2008 Central Park production of “Hair” — and she has enough raw, unforced ebullience that when the audience chimed in on the choral parts of the Motown hit “My Guy,” it didn’t feel hokey.

That sincerity went a long way, but Miller also displayed musical smarts as she girlishly crooned “Someone to Watch Over Me” in long, soft phrases that always felt emotionally specific. In general, she stayed close to the melodies — she’s a pop creature, not a jazz voyager — though Sampliner’s arrangement of “Little Girls” from “Annie” sounded a lot like the piano line from Steely Dan’s “Home at Last,” with Miller delightfully biting off the tart lyrics and soaring into Miss Hannigan’s comically bitter fantasia.

The Broadway fare included Stephen Sondheim’s “No One Is Alone,” served up gospel-style, plus generally straightforward selections from “Hair” and “Sister Act,” which earned Miller a Tony nomination in 2011. Vocally, Miller’s calling card isn’t a stage belter’s explosiveness at the top of the range; instead, she’s a smooth, sprightly singer with great pitch, a mellow tone and theatrical savvy.

Patina Miller fumbled her lyrics during an encore, but her singing won over a Kennedy Center audience. (Courtesy Kennedy Center)

That savvy is still being buffed. Friday was Miller’s first concert ever, and at times it showed, especially after that generous but sloppy second encore. As Sampliner and the rest of the quartet (guitarist John Benthal, bassist Mark Vanderpoel and drummer Rich Mercurio) vamped through the fabulous barrelhouse arrangement of “Miss Celie’s Blues,” Miller beamed at the crowd and danced but couldn’t figure out how to use this exit music to get off the stage. You wanted someone to whisper in her ear: “It’s okay, dear — you’ll definitely be invited back.”