Jazz Fest does many things; rarely is one of them rock. For much of the festival’s 35 years, rock was neither a jazz nor heritage music and didn’t often make the cut.

Lenny Kravitz has been one of the few exceptions, and Sunday afternoon on the Acura Stage he was the prototypical rock star--charismatic, in charge, and stylish in a fashionably ripped T-shirt and distressed jeans. Like his music, Kravitz and his band’s look is deliberately rooted in ‘60s and ‘70s rock, soul and funk.

He opened with the guitar-heavy riff rock of “Dirty White Boots” and his cover of The Guess Who’s “American Woman,” which got the set off to blistering start. After that, heaviness was a tool he deployed when an energy boost would help. “It Ain’t Over ‘til It’s Over” chilled the energy so he revved it back up with “My Mama Said.” When that song’s lengthy, wandering jam section dissipated the energy, he ramped things up again without”Let Love Rule.”

The jam and extended sing-along version of “Let Love Rule” punched his Jazz Fest card with their open-ended structure of a piece with the city’s improvisational vibe. Musically, the latter lost energy as the song went on, but Kravitz compensated with the theater of an extended trip into the audience and through the crowd. He made it through unmolested to once again lead the sing-along. that time with more enthusiasm from the crowd.

Kravitz’s show wouldn’t work without his star power. His lengthy digressions would be intolerable from anyone less engaging or with a less professional band. Tracks wandered, but the band stayed steady and committed to whatever Kravitz wanted.

“Are You Gonna Go My Way” closed the show on a hard note, and to the surprise of almost no one, Kravitz brought out Trimbone Shorty with an arm around his shoulder. Shorty played in Kravitz’s band in 2005, and he broke off a electric, raunchy solo that perfectly suited the song and the moment.