There’s something about the music of Arvo Pärt that makes people stop driving. In the late 1970s, the record producer Manfred Eicher heard it on the car radio and pulled off the road to listen until it was over. In 1984, Toomas Hendrik Ilves, the future president of Estonia, at the time a college professor in Canada, heard on his car radio the recording Eicher had subsequently released. He pulled off the road in his turn. Ilves told his story to the audience at the start of a remarkable free concert of Pärt’s music at the Kennedy Center Concert Hall Tuesday night that made everyone in the concert hall, though not driving, certainly stop, listen and marvel.

The audience was primed to be enthusiastic. When Garth Ross, the Kennedy Center’s vice president for community engagement, mentioned in his pre-concert remarks that the composer was present, the crowd — and how many living classical composers can fill a 2,400-seat concert hall? — rose to its feet with a prolonged standing ovation, until the 78-year-old composer, bearded and slight and looking more like a rumpled professor than the monk with whom he is often compared, rose from his seat in the balcony with gestures of acknowledgment. “That doesn’t happen every day,” Ross observed when the noise had died down.

Nor does it happen every day that an audience gets to hear such stunning performances — by, in this case, the Estonian Philharmonic Chamber Choir and the Tallinn Chamber Orchestra, under founder Tonu Kaljuste — of such strong music.

I recently wrote that Pärt appeals both to classical and non-classical audiences, not least because he epitomizes a spirituality that gives his music a sense of a greater meaning without crossing into mere New Age-y effect-mongering. Yet this concert made me think that, popular though his music is, it may still be underestimated. I’ve heard some people in the classical world aver that Pärt is a one-trick pony, using the technique he calls tintinnabulation, which involves juxtaposing a melodic line with its related triads, to write music of arresting simplicity, offering spirituality rather than sophistication. Anyone who was present on Tuesday can testify that this claim is false.

All of Pärt’s music is easily identifiable, it’s true; like most great artists, he has a clear set of fingerprints. But each of the four pieces on Tuesday’s program, especially the relatively brief “Cantus in Memory of Benjamin Britten,” was a world of its own, from the dramatic string stabs and dark male voices in “Adam’s Lament” (the most recent work, written in 2009) to the repeating, descending, aching, intensifying phrases of the “Cantus,” touched by the pure and wistful tolling of bells. And while spirituality is central to his life and music, Pärt is no more or less a “religious composer” than Bach — whose pure and brilliant Passions Pärt’s “Te Deum,” the final piece on Tuesday’s program, called to mind.

There’s nothing superficial about Pärt’s music; it’s steeped in a profound knowledge of the vocabulary of the Western canon, reaching back to the medieval plainchant that it so audibly evokes. Pärt simply takes the same data as many other composers — the instruments of the orchestra, the voices of the chorus — and arrives at his own unique conclusions.

Another rare thing about Tuesday’s performance: hearing performers who are expert in a living classical tradition. The classical world has a number of European ensembles that are steeped in the music of composers they’ve been playing for centuries. Seldom, though, do you hear groups that have come to world renown with a tradition whose creator is sitting in the audience.

Kaljuste, a towering figure who looks a lot like Liam Neeson and, as he ages, also like Franz Liszt, conducts with an authority that translates his gestures into sounds. At one point in the “Te Deum,” he extended the fingers of an already-upraised hand and you could hear the subtle change in sound in the men’s chorus, exactly corresponding. He has led most of Pärt’s major works in their world premieres and first recordings, and he and the players offered expertise and flexibility, coupling the majesty of some of the larger moments in the music with a sense of intimacy that’s very much in keeping with Pärt’s work.

The least compelling performance was the opening piece, “Fratres,” one of many versions of one of Pärt’s best-known works. It was played — I think deliberately — with a straightforwardness that was the antithesis of the heightened emotion many bring to this juxtaposition of seesawing violin patterns (played with gentle clarity by the concertmaster, Harry Traksmann) and organ-like string chords, but came off as slightly nonchalant. Playing without pathos, however, is generally a virtue in this music. One of Pärt’s frequent effects — in, for instance, “Adam’s Lament” — is having the strings seem to be drawing breath, like a supportive bellows, beneath a clear unspooling vocal line. This keeps a sense of the human in music that, however spiritual, is very much of this world.

It was the first of four Pärt concerts in Washington and New York and an extravagant gift to an audience that, representing all ranges of age and sartorial taste, greeted it with the ardor of a rock-concert crowd, whooping and clapping and holding up cellphones to capture videos of the performers’ bows when the music had finished.

The gift wasn’t restricted to those present, either. This concert was jointly presented by the Estonian Embassy (the ambassader, Marina Kaljurand, led fundraising efforts herself) and the Kennedy Center’s Millennium Stage. Like all Millennium Stage performances, it can be seen, in its entirety, as a video on the Kennedy Center’s Web site. Just don’t try to watch it while you’re driving.

The Arvo Pärt Project series of concerts continues with a performance on Thursday at the Phillips Collection (sold out) and performances in New York at Carnegie Hall (Saturday) and the Metropolitan Museum of Art (Monday).