Revisiting ‘A Man Under the Influence,’ Alejandro Escovedo plays with a purpose

Alejandro Escovedo played his 2001 album in its entirety Sunday at City Winery.Katherine Taylor for The Boston Globe

Alejandro Escovedo likes songs with stories, and at City Winery Sunday night he was the American story.

Born in San Antonio, Escovedo, now 67, came of age as part of the first wave of American punk, with his band the Nuns opening for the Sex Pistols (and playing the Rat in Boston, he told the crowd). He honed his songwriting craft with the band Rank and File in the fertile ’80s Austin music scene. His musical Mexican-American family includes his brothers Coke and Pete Escovedo, and Pete’s daughter Sheila E.

Of particular import Sunday was another chapter of his story — a 20-year battle with hepatitis C (now cured) exacerbated by a lack of health insurance. The show was part of a short tour, called Think About the Link, for the Prevent Cancer Foundation, to raise awareness of hepatitis B and C, as well as HPV, and their connection to that disease.

Musically, the show wove together multiple strains of Americana, plus a couple of apt Britishisms. The focus of the tour is Escovedo’s highly regarded 2001 album, “A Man Under the Influence,” played in its entirety, and the band included the producer of that album, Chris Stamey, as keyboardist and musical director. (Stamey also played a short, intimate opening solo set.)

To give you an idea of the rich breadth and pedigree of this show, the love song “Rosalie” combined trumpet-fueled Tejano-dance lilt with 12-string guitar-pop jangle, the latter courtesy of one of the people who, along with former dB’s band member Stamey, helped invent it, Mitch Easter (of band Let’s Active, as well as a producer for R.E.M.).

The “Influence” portion of the show was broadly encompassing throughout — Tejano rock, country blues like “Rhapsody” (the latter with a whining pedal steel, courtesy of Eric Heywood), the death-haunted border ballad “Across the River,” and the full-on rocker “Castanets.”

Complementing the orchestral breadth of the album, Escovedo and Stamey put together a band augmented by that trumpet as well as viola and cello and two backup singers. Thanks to Stamey, textures remained clear and balanced, no matter how busy the action, even when strings and guitars overlapped in crosscurrents of melody and rhythm.

The encore portion of this two-hour set was dedicated to people lost to cancer, and included David Bowie’s “Moonage Daydream” and Bowie’s song for Mott the Hoople, “All the Young Dudes,” which Escovedo encouraged the audience to sing along to, “for the memory of someone you love.” It was a show as big-hearted and generous as they come.

Alejandro Escovedo

With Chris Stamey

At City Winery, Boston, Sunday night