Conductor Yannick Nezet-Seguin and the Philadelphia Orchestra. (Jessica Griffin)

Yannick Nézet-Séguin is really an awfully good conductor.

He’d better be. He recently extended his contract with the Philadelphia Orchestra through the 2025-2026 season. And he’s about to take over as music director designate of the Metropolitan Opera. The music world, in short, has crowned the 41-year-old one of its darlings, with the tacit but heavy responsibility of saving classical music by carrying its major traditional institutions into the future for a next generation. It’s a lot to ask of someone who, however charismatic, gained his position simply by conducting very well.

Despite the hype around Nézet-Séguin’s youth and dynamism in Philadelphia, not much of the flash of the new is evident in the programming of the orchestra’s Washington visits. Its Kennedy Center performance on Tuesday night, courtesy of Washington Performing Arts, was another in a long string of Philadelphia programs about which I could write, and have written, that I wasn’t thrilled at the prospect of hearing the repertoire, but they did a terrific job bringing it across.

Nézet-Séguin’s mettle was shown best in a fine “Petrushka,” driving and vital from the first notes, with every detail of the orchestration and every solo picked out in vivid carnival colors like an early Kandinsky painting. In Nézet-Séguin’s reading, it was easy to hear the piece as an antecedent of “Rite of Spring,” with its skewing zigzag rhythms and folkloric force. But you could also hear all the characters, limned with such vividness that they seemed to be dancing above the stage: the delicate ballerina, the jesterlike figure of Petrushka (a Russian equivalent of the Punch of Punch and Judy fame), thumbing his nose at the world in brassy flourishes.

Much weight is placed these days on the importance of telling stories in art — indeed, it seems to have become a buzzword for what administrators hope art can give to audiences, invoked in the past couple of days by Gianandrea Noseda about his inaugural season with the National Symphony Orchestra and by Stephanie Stebich, just named the director of the Smithsonian Museum of American Art. They’re not alone. “Telling stories” is precisely the reason a story-ballet such as “Petrushka” gets programmed so often (the Philadelphians last brought it to Washington in 2010). But in it, Nézet-Séguin showed authority and clarity without excess.

If we’re going to tell stories, let’s find some new ones. The Philadelphians’ home run in this regard was the unannounced “amuse-bouche,” in Nézet-Séguin’s words, that opened the program: “D’un matin de printemps” by Lili Boulanger. The story of this piece, if you want one, is that Boulanger died in 1918 at 24 , leaving a few works and a champion in the person of her better-known older sister, the teacher and composer Nadia. Its story is also that it’s a wonderful, energetic work: Spring, in this narrative, is a fertile, aggressive time filled with motion and light, with the flavor of French impressionism and the vivacity of a young new voice. This is exactly the kind of thing we should be hearing more of, and the kind of thing that could interest a new audience, particularly when it’s played with such golden depth.

The program’s scheduled opener, which followed, was Chopin’s first piano concerto, played by Louis Lortie with a demure liquid elegance. The orchestra, at the start, got a little tangled up in the attempt to balance Nézet-Séguin’s propulsive urges with the need to maintain a certain delicacy and restraint, but supported, in the end, a lovely reading of a piece whose story is about skill and shedding light across the darkness.