Anyone who has caught a Rolling Stones concert in the past 25 years should remember Lisa Fischer, at least for going toe-to-toe with Mick Jagger to ignite “Gimme Shelter.” Fischer’s steady Stones gig highlights her career as an A-list backup vocalist, a track record that earned her a featured role in 20 Feet from Stardom, an Oscar-winning 2013 documentary on those stars in the shadows.

So it’s not surprising that Fischer dips into that Stones catalog when she performs with her band, Grand Baton. However, Fischer bends every song to her own genre-blurring whims, caressing each phrase with pinpoint subtleties and dynamics. And then she drops more unexpected choices, like Led Zeppelin’s “Rock and Roll.”

Unlike Jagger, Robert Plant could flat-out wail, but Fischer’s soulful reinvention of that song over a slinky Caribbean-jazz groove can astound, especially when she leans toward an echoey second microphone to spin the word “lonely” into the stratosphere.

“It’s like playing with clay,” Fischer explains from New York with a dreamy, childlike cadence. “There are no rules. It’s like we have so many rules to live by all the time. It’s just so freeing and so refreshing for the soul. It’s playing. Not worrying. Trust the moment and just share that trust with everyone. It’s so fun for me.”

Indeed, Fischer exudes a Zen-like sincerity and appreciation for what she does. Her warmth on the bandstand during a sold-out, four-show December stint at Scullers Jazz Club made everyone in the room feel like an old friend, while her Facebook page reveals a personalized reply to nearly every fan’s comment.

“I’m just thankful I get to sing anywhere,” says Fischer, who returns to play the Wilbur Theatre on April 5, as well as Northampton’s Calvin Theatre on March 31 and the Newport Jazz Festival on Aug. 1.

Much of her current appeal could be attributed to 20 Feet from Stardom, which profiled Fischer and peers such as Merry Clayton (who recorded “Gimme Shelter” with the Stones) and Darlene Love. “It’s allowed me a second chance, a second life, a second chance at a life—because I’m getting up there,” says Fischer, 56. “Even though in my mind, I don’t feel like an age, the time is ticking. Your body changes and things change, so I can’t be the rocker chick that I was at 27.”

Actually, at that age, Fischer was an R&B/soul chick, enjoying her big break as a backup singer for mentor Luther Vandross. “He cared so much about every single aspect of what he was presenting to the audience,” she says. Fischer broke from the background to release a 1991 solo album, So Intense, yielding the Grammy-winning No. 1 R&B hit “How Can I Ease the Pain,” which she still performs.

Yet Fischer never finished a follow-up amid questions of direction. She returned to supportive jobs, performing with Tina Turner, Sting, Chris Botti and Nine Inch Nails, in addition to the Stones. “It’s like sewing together a beautiful quilt and feeling like I’m a part of the thread,” she says. “I love that role, and it’s always exciting to watch [those artists] blossom.” She doesn’t yearn to run the show.

“There are so many people that really desire and need and have a vision to be in that place,” Fischer says. “I’ve had the gift of having a [record] deal. Then being able to record music with so many wonderful people—and have people react to it—was a gift… The mistake would have been daydreaming about doing a record again.”

Partly because the acts that she mainly works with haven’t been recording either, Fischer has focused on the stage. “That’s what’s most present and real to me at the moment,” the singer says. And she’s found empathetic foils in Grand Baton guitarist/director JC Maillard, drummer Thierry Arpino and bassist Aidan Carroll.

“They know how to listen and toss the ball back and hold hands,” Fischer says. “You feel it, but it’s not something that they speak. They just are. That was the most important thing for me, just having the right energies around me.”

Lisa Fischer & Grand Baton play the Wilbur Theatre on April 5.