Throughout his career, retiring principal Peter Boal has come to define the title role of “Apollo.” Saturday evening marked his final performance in a work that was also a “turning point” in Balanchine’s career as a choreographer.

To a score by Stravinsky, “Apollo” depicts a nuptial between music and dance in the shape of Apollo and Terpsichore. Guest conductor Paul Mann guided the magnificent score, which conjures Apollo’s mountaintop home of Olympus with an ethereal melody and rocky percussion.

The curtain lifted on Mr. Boal in a valiant fourth position, playing the kithara in wide circular strokes. The circular theme is repeated throughout the work: In the solo of each Muse, the ring combinations when they dance together, the persistent round port de bras, and, eventually, in the closing measures, as the sun itself rises in the east.

As the cello plucks down the scale, Mr. Boal nimbly steps down the stage. The Muses enter from three corners with alternating battements. He touches each of them in turn, fulfilling a lovely canon pattern. To each he assigns their respective duties: Calliope, as the muse of poetry, receives a tablet; Polyhymnia, as the muse of oratory, receives a mask; Terpsichore, as the Muse of dance, receives a tortoise lyre.

Together they interlock arms in delectable symmetries. They heel-walk in tandem, holding one another’s chins like figures on a processional frieze. But it is Terpsichore (literally, one who takes “pleasure in the chorus”) who reverently approaches Apollo in her solo. Apollo’s own solo follows.

On Saturday Mr. Boal enunciated each movement with boldness and dignity in a series of combinations that have become second nature to him. Stretching one arm high and wrapping the other around his waist, he flashed his fingers in quick expressions of his potency as the sun god.

As always, he let the splendid choreography of Balanchine shine through. Apollo has been struck by the exuberance and grace of Terpsichore. His broad diagonals become increasingly agitated until he finally crouches down, holding out an index finger behind him. It is graciously met with Terpsichore’s own finger. She steps over his arm and takes a noble seat on his knees. Music and dance sublimely embrace.

On Saturday Terpsichore, played by Yvonne Borree, put her elbows in Mr. Boal’s palms. He laid his head on her hands. Her body elongated and stiff, he lifted her up and carried her around with him like a giant instrument. In his divine hands, she came alive again.

***

Jerome Robbins’s “N.Y. Export: Opus Jazz,” revived by New York City Ballet Friday evening, delivers an abstract portrayal of arrested development, circa 1958. But the work is a far cry from the Fonzie, or, for that matter, Mr. Robbins’s own “West Side Story,” created only a year earlier. Instead the choreography has the striking, irreverent design of physical graffiti sprayed across a classical facade.

Uproarious, scandalous, and affirming, “N.Y. Export: Opus Jazz” captures the generational tension of a certain class of youth, which, seizing novel forms of music, uses their sexuality and dance moves to make physical statements. In Robert Prince’s addictive score, various styles of modern jazz are assembled to complement the different sections of the work, whether the Duke Ellington’s stride sound (“Entrance”), the Afro-Cuban percussion of Dizzy Gillespie (“Statics,” “Theme, Variations, and Fugue”), or the cool whispering of Miles Davis (“Passage for Two”).

To the brash sound of horns, a gang of 17 teenagers loiters about, staring derisively at the well-to-do audience in front of them. At the drop of a hi-hat, they strike perpendicular poses before settling into a steady, uniform oompah. The dancers’ movements are full of surprises; each joint seems to pop with syncopation.

Forming parallel lines, the ensemble does a little soft-shoe, their wrists hanging limply in front of them. The men take the women and swing them in the air once, twice, and then completely over, the whole time following the walking bass line. Members of the ensemble grab hold of one another and rotate in deep crouches. Huddling together, they form a united front. A single beam of light is a furtive, nearly transcendent description of escape.

The pace quickens in the second section, “Statics,” when five men, led by Seth Orza, spin at lightning speed to the drummer’s cymbal. In a gripping performance, Rebecca Krohn enters, models flirtatiously, and elicits from the men brief variations on pent-up frustration. They scrub their heads and hug their fists before gathering together to launch her off stage.

For “Improvisations,” we gather in a schoolyard behind a sloping cement embankment. This isolated after school hang-out spot is a place for showboating solos and random hookups. Making a space in the middle of the crowd, individuals and groups gyrate robotically or tangle themselves up in humorous contortions. Mr. Robbins gives himself an opportunity to exercise his particular gift for the male swoon (a la “Fancy Free”). One group of men participates in an outrageous promenade, holding onto one another’s heels as if in a jungle gym.

The contemplative, mesmerizing “Passage for Two” departs most elaborately from the Jets and the Sharks of “West Side Story.” In this painterly duet, Rachel Rutherford and Craig Hall rendezvous in a dark corner. Incrementally, they discover each other’s bodies in a youthful intimacy. He takes hold of her hip; she slowly swaggers to the lone cry of a muted trumpet. They throw their arms around each other tightly and dip to a crouching position.

If there is a desperation in their behavior, there is also triumph, as Ms. Rutherford unfolds into a straight limbed X. Balancing on the back of Mr. Hall’s shoulders, she is lifted up, remains there for several suspenseful measures, comes down, and they both walk away.

The concluding section, “Theme, Variations, and Fugue,” revisits gestures of youthful defiance – the challenging step, a shrug, finger-snapping – with an emphasis on complex structures of classical music and ballet. In contrast to the previous section, the vibraphone-filled music was almost ticklish at times. The dancing tended to be more physical and acrobatic. The men picked the women up and pushed them forward and back like paintbrushes, before spanking them impudently to the mambo rhythms.

Mr. Robbins originally developed the work for his short-lived touring troupe “Ballet: U.S.A.” But this NYCB premiere owes its success to the combined efforts of an A-list collection of collaborators. Edward Verso, who danced in the original, gave the work an air of period authenticity in his expert staging. Jennifer Tipton brought her seasoned touch to the lighting design.

Ben Shahn’s lithographs of abstract design (colorful globules), commercial collage (slogans), and industrial cityscapes (a backdrop resembling out-of-focus power lines) contribute to a lingering mood of urban alienation. The outfits, designed by Tony-winner Florence Klotz, are brightly colored tops over black tights and white sneakers. While richly suggestive of a place and time, the restaging of “N.Y. Export: Opus Jazz” transcends both with exquisite artistry.

“Apollo” will be performed again May 7 & 10; “N.Y. Export: Opus Jazz” will be performed again May 3, 5 & 7 (Lincoln Center, 212-870-5570).