Meshell Ndegeocello outlined a catalog of social and natural disasters at one point in her sold-out show at the Highline Ballroom on Wednesday night. “You turn on the telly and every other story/Is tellin’ you somebody died,” she sang in her deep-shadow vocal register, a notch or two above a murmur. The tune was “Sign o’ the Times,” by Prince, rearranged for upright bass, pinging keyboards and hazy rhythm. The overhaul affected everything but melody and lyrics, amplifying the bitterness in the song.

Prince, an artist of seemingly endless resources — both musical and material — poses a slippery challenge to any would-be cover band, even one with purely imitative aims. (You know this if you’ve ever been at a wedding reception wincing through “1999.”) Digging deeper than outright imitation, meanwhile, requires both connoisseurship and independence, a sense of identity strong enough to survive immersion in the songs.

None of which is a problem for Ms. Ndegeocello, a singer-songwriter drawn to the darker side of funk, and to a tough-minded brand of introspection. Occasionally during the show she took the audience into her confidence, divulging her history with a song: “My mother and father thought I had lost my mind,” she said about her obsessive playing of “Controversy.” This just after strutting through that tune, more or less faithfully, with close attention to sonic detail.

She was backed by a slightly modified version of her razor-sharp band: Chris Bruce on guitar, Keefus Ciancia on keyboards, Mark Kelly on bass and Deantoni Parks on drums. They nailed down every groove, with more earthiness than on the originals. Intense but restrained, stylishly somber in all black, this was a group no one would mistake for Prince’s. Its precision was too workmanlike: pro-virtuosity, anti-flamboyance, more efficient than ecstatic.

Of course it was Ms. Ndegeocello who set that tone, singing with a dark, stoic clarity and only rarely picking up the electric bass, her most dazzling instrument. She saved her boldest moves for the song choice, heavy on early album tracks like “Something in the Water (Does Not Compute),” “Annie Christian” and “Lady Cab Driver,” remade from a bass-popping funk tune into an ethereal, brooding meditation. “I don’t know if I can last,” she sang repeatedly as the song wound down, and it was only then that she dug into a bass riff, sounding both determined and woozy.

She cast similar spells in “Purple Rain,” its chorus outfitted with an ominous new chord progression, and “I Wanna Be Your Lover,” arranged for strummed acoustic guitar. And“I Would Die 4 U” came stripped to its essence, underscoring the poignancy of the lyrics, with their sacrificial pledge. Ms. Ndegeocello sang that one quietly, but not dispassionately.