Live music doesn’t get any more intimate and inviting than when Eugenia Zukerman, the flutist, and David Leisner, the guitarist, step onto the stage. Under the auspices of the Maine Center for the Arts, the classical — as well as classy — duo appeared Sunday at Minsky Recital Hall to deliver a chamber music concert filled with rigor, lyricism and warmth.

As virtuoso instrumentalists, Leisner and Zukerman have fine-tuned their artistic collaboration into a powerful unity. The outcome is superbly satisfying interpretations of works such as Handel’s Sonata in A minor and Bela Bartok’s Romanian Folk Dances. Both were played with rich tones and full-hearted musicianship.

But a mutual love for performance and elegant sound is the hallmark of the Zukerman-Leisner combo. When they approach a piece together, a distinctive and ageless quality takes over, and the stage transforms into their playground, the instruments their toys, the music their delight. Leisner and Zukerman are world-class, a well-known fact reinforced by Sunday’s performance. But they are genuinely effusive in their art, and it’s infectious when in full spin.

Which it was, in particular, during Mauro Giuliani’s Grand Sonata in A Major, a gifted-and-talented piece if ever there was one. Filled with zesty passages and elaborate textures, the Grand Sonata seems as if it were written specifically for Zukerman and Leisner.

“Fish Tale,” by Argentina-born composer Osvaldo Golijov, actually WAS written last year for Zukerman and Leisner. This little vignette swims along, winsomely revealing a fish adventure. Golijov subtitled it “watercolor for flute and guitar” — a perfectly apt description of this picturesque minimarine history.

Although Zukerman, more than 25 years into her career, is the headliner of this team, Leisner gave a formidable reading of Bach’s Prelude, Fugue and Allegro (BWV 998). Somewhere early in the second section, Leisner really took off with style and authority. He’s masterful and he landed right smack in the heart of this piece.

The concert ended with the first and second segments from Astor Piazzolla’s “Histoire du Tango” — a fitting finale to a program by a musically seductive twosome.