"Happy birthday to me," Mavis Staples sings vampily. "How old am I? Sixteen years old." In fact, she turned 75 today, but 16 feels about right. The gospel/soul great is one of the few voices of the civil-rights era still to be touring, and while there's gravelly gravitas to her vocals and her swaying hips, her fire is undimmed. A belated Grammy winner for the 2011 album You Are Not Alone – her 13th solo record in a career that started in 1950 with the Staple Singers – she wears her stature lightly.

Backed by her sister Yvonne on vocals, longtime guitarist Rick Holmstrom and a crack band, she's commanding yet playful. The struggle that inspired her father to write Freedom Highway in 1962 – performed here as a rootsy stomp – goes on, but Staples is also in this for the joy of it. For every broodingly spiritual I Like the Things About Me, there's a buoyant If You're Ready (Come Go with Me); a foreboding cover of Buffalo Springfield's For What It's Worth is balanced by the flirtatious interplay between her and a backing singer on Let's Do It Again. "I'm not a girl that could linger, but I feel like a Butterfinger," she purrs at him, and he smiles swoonily, as would any mortal man in the presence of such supreme female self-possession.

Staples's voice is still amazingly rich, but its lighter tones are also beguiling. Trilling the chorus of Pharrell's Happy, she sounds like the 16-year-old she never left behind – though the teenager in her is swept aside by the grande dame for the show-closing I'll Take You There. "We've been taking you there for 64 years!" she shouts, and you wouldn't bet against her being around for another 64.

• At Mostly Jazz, Funk and Soul festival, 12 July. Box office: 0844 870 0000. Venue details: Moseley Park, Birmingham.