Marris Jansons led the Royal Concertgebouw Orchestra in a searing performance of Mahler’s First at the Kennedy Center. (Anne Dokter)

The Royal Concertgebouw ­Orchestra has been called the best in the world. It has everything: gorgeous sound, flexibility, a long and august tradition of high-caliber music-making under great conductors. The orchestra’s performance at the Kennedy Center on Tuesday night, part of a 125th-anniversary tour that will take it to six continents this year, did nothing to diminish the reputation that had preceded it.

Along with everything else — rich strings, shining brass, acute percussion — the orchestra has one of the world’s best conductors, Mariss Jansons. Latvian born, Russian trained, slightly stooped but lithe and energetic at 70, Jansons is the contemporary embodiment of the old-school conducting tradition in which an artist spends his life delving more and more deeply into his scores, honing and polishing and perfecting in an unattainable quest for excellence. This is a romantic notion of music-making that sounds too good to be true, but it’s the only way to begin to describe the performance of the Mahler First Symphony that finished the program: Jansons and the orchestra have both played this piece dozens, hundreds of times, and this performance grabbed you by the throat.

Such repetition has helped give Jansons something of a reputation for traditional programming, and though that reputation has been belied by some of his recent choices with both the Concertgebouw and the Bavarian ­Radio Symphony Orchestra, the other elite orchestra he leads, the Concertgebouw’s current U.S. visit will tend to uphold it. The orchestra is playing pieces with which it has had a particular association in its history. Mahler is one of its cornerstones, an association developed during the 50-year tenure of Wilhelm Mengelberg, during which Mahler himself often conducted the orchestra.

As for the first piece on the program, Bartok’s Second Violin Concerto, the orchestra gave it its world premiere in 1939. It’s a big, juicy showpiece for orchestra and soloist — here, the violinist Leonidas Kavakos, looking like a Greek Hiawatha with his shoulder-length black hair, and sounding like a worthy partner for an elite orchestra, with a golden tone and an easy command of this concerto’s challenges that matched the intense insouciance of Jansons’s approach. There’s a lot of big playing in this quasi-romantic piece, which ranges through the whole compositional bag of tricks, from the theme and variations of the second movement, opened here with meltingly sweet playing, to a genuine 12-tone row in the first movement, which Bartok did just to show that he could. Kavakos brought fire aplenty to the skitterings of the final movement — itself a variation on the opening movement — but the urbane restraint he brought to the second movement was even more notable.

Still, the Mahler was the highlight. Including it on the program was tantamount to a classic band offering its greatest hit; except that there was nothing routine about a performance that was intense from the start and, finally, revelatory. Jansons’s style has always been to let the music speak for itself. He’s a mercurial and energetic conductor, visibly connected to all his players, often palming his baton so he can conduct with hands alone before shifting it again into his fingers, exhibiting a continual, even kinetic restlessness. His performances are searing without involving pathos. On Tuesday, the Mahler grew progressively toward a fourth movement that blazed with emotional depth and profundity, never taking the obvious route, holding back on big themes, or, in one reprise, playing with such restraint, yet without losing intensity, that it was as if a wall of glass had suddenly descended between stage and audience, letting us remember the glories of a performance even before it had ended. Jansons offered a whole spectrum of degrees of loudness, as well, and having pulled out all the stops briefly to show just how loud the group could get, held ever so slightly back at the close, so that the snaps of the final chords had room for a little extra bite.

The concert was presented by the Washington Performing Arts Society, and the one thing that detracted even slightly from a near-perfect evening was the video screen over the stage showing slides of coming attractions and “fun facts” before the show, as if classical music might extend its reach by emulating a movie theater. It was a wrong note on a night that abundantly demonstrated the glories of tradition.