Pekka Kuusisto. (Kaapo Kamu/Handout)

The Phillips Collection was once a private home. On Sunday afternoon, the violinist Pekka Kuusisto and the composer-pianist Nico Muhly used it to offer a world-class house concert.

Technically speaking, it wasn’t a house concert. It was the usual Phillips Collection Sunday afternoon performance. But the two musicians brought a sense of such intimacy and spontaneity that a listener felt more a participant than a passive recipient. Each movement of Bach’s second partita, for instance, began as if it were a completely fresh idea that happened to have struck Kuusisto as he stood by the piano. Each progressed as if he were thinking his way through it, musing on what might come next. This music felt every bit as new as the two works by Muhly, one a four-movement essay (“Drones & Violin”), one a shorter sally (“Drones & Piano”).

And it’s a rare performer who can polish off the Chaconne, the final movement of the second partita and one of the towering monuments of the violin repertory, and then flip his Guadagnini around and start strumming it like a banjo as he sings Finnish folk songs. Indeed, it’s a rare performer who can make you want to listen to a Finnish folk song after you’ve heard the Bach — something of which Kuusisto was perfectly aware. “It’s worth staying for,” he told the audience, drawing a laugh.

It was an exquisitely balanced program. Each Bach movement was answered with a work by a living composer, all presented as flip sides of the same coin — so that the end of the Bach Gigue, an exhalation, was immediately followed by the inhalation of the start of Muhly’s second “Drones” piece, in a seamless continuum.

Kuusisto got the attention of Washington audiences with his performances of the Lindberg violin concerto last year with the National Symphony Orchestra. But he didn’t play like a soloist here — more like a poet. The initial movements of the Bach were free of preconceptions about beauty or evenness of sound; they were, instead, an expressive sequence of meditations. They were thus perfectly calibrated to Arvo Pärt’s “Fratres” — one of many versions of this quiet, intricate work, which drifts and tangles a sequence of variations around a six-bar theme. And it yielded naturally to Philip Glass’s “The Orchard,” in which Muhly’s buoyant, elastic playing lent an extra urgency to the repeated three-note skipping figure in the piano.

Nico Muhly. (Matthew Murphy/Handout)

Muhly is well known as a composer, having most recently made waves when the Metropolitan Opera opened his “Two Boys” last fall. Both of his pieces here were excellent — and they brought his arresting pianism, a less-known arrow in his quiver, to the fore. In a program that had been characterized by repeating patterns, drifting notes and a sense of restraint, the piano suddenly thundered out in a fortissimo, tearing open the mood of the afternoon, revealing a Romantic heart within the afternoon’s patterned, shifting, gentle musical idiom. After the outbursts, Muhly scaled back down, promptly — nothing to see here, folks — but his playing was still all bright colors and high contrasts, albeit hidden in the shades of the dappled musical landscape of the performance as a whole.

Kuusisto, too, couldn’t help showing his hand as a brilliant player, even if the afternoon — by his admission to the audience — was not designed to showcase virtuosity. In the Bach Gigue, between the two Muhly pieces, the quick fingerwork unsheathed a clean, firm sound, like a swordblade, gleaming with light. And the Chaconne partook of both the brilliance and the subtlety.

Often, the final pieces on a program, particularly if they’re in a performer’s own language, convey a sense of relaxation, a look behind the curtain. But the two improvisations on Finnish folk songs that ended this performance seemed rather a seamless extension of an eclectic yet perfectly organic collection of music. The curtain had been down all along. So if Kuusisto chose to strum on his violin and burst into song while Muhly wandered along the edge of a precipice on the keyboard beside him, it was the most reasonable thing in the world. More concerts should end this way — and start this way, and continue this way. If only more musicians were able to pull it off.