It was destiny, it was church. Nina Simone was called "the high priestess of soul" and the musicians and audience gather to pay homage, if not worship. They leave uplifted by four exhilarating African-American singers.

Sing the Truth is a tribute to the feisty, brilliant jazz diva, led by Simone's daughter. Christened Lisa, she has courageously taken "Simone" as her stage name, recruited three of the most acclaimed voices in popular music, and made her mother's legacy her life's work.

They take the stage separately, in ascending order of seniority. Youngest – and quickly on track to becoming the audience favourite – is up-and-comer Lizz Wright. She stands stock still in front of the subtle, sophisticated jazz quintet, looking demure. Unaccompanied, she begins: "I loves you Porgy..." Then, a pause. The audience is instantly riveted by her velvet vibrato, which her hand gestures seem to tease from deep in her diaphragm.

Simone – the daughter – sashays on to a vamp, in a cerise sari bought in Wellington that morning. If her entrance conveys she has something to prove, her voice says otherwise: it is suited to Broadway but not strident, and delivered effortlessly. Sing the Truth is both celebration and cutting contest.

Happy to oblige are the evening's two divas, Grammy-winners both: Patti Austin and Dianne Reeves. Austin is a soul-testifier, who asks for a witness in a slinky Trouble in Mind. She works the room with charm not corn, and finds the audience quick to respond. To a lightly stepping piano, Austin grins. "You know where this is going." She plays with My Baby Just Cares for Me, whistling the melody, refreshing it with contemporary celebrity references.

In blue vestments, Dianne Reeves looks like Diana Ross in her lost gospel period. Be My Husband is taken like a field holler, to a slow rhythm, and her voice rings around the room. Reeves sings her way off stage, knowing she has upped the ante.

And so it goes, classics such as Young, Gifted and Black and I Put a Spell On You all conveyed with humour, love and flair: but none of the show-off gymnastics beloved by Idol contestants. This is a music night, not a nostalgia show or polemical statement.

Nina Simone's politics – her feminism, her civil rights activism – are present but not correct. The singers make their point, with the same delicacy and drama as the band. "Everybody say it!" (Yes!) "My name is Nina." (Nina!) "Thank you for lifting us up!"