Tango takes two, and the foremost tango dancers tend to travel the world in pairs, demonstrating and teaching. (Most are based in Buenos Aires, but trace any tango couple on YouTube: You find their appearances in Warsaw, Hong Kong, Rome.)

Gabriel Missé, surely the most exceptional tango dancer of recent years, and his current partner, Carla Espinoza, are in New York, this week and next. His previous partnerships have been with Natalia Hills and Analía Centurión. (He danced twice with Guillermina Quiroga in 2015-16 in New York, but nowhere else.) He remains one of our era’s superlative dancers of any genre; on Wednesday, at the Argentine Consulate, I had my first chance to watch him with Ms. Espinoza, with whom he has been dancing since 2015.

Though Mr. Missé never deviates from the style of traditional tango, each of these partners has brought out a different quality in him. He seems naturally happy, sparkling, often funny; Ms. Centurión matches his temperament this way, whereas the more poised, brooding, sometimes tragic Ms. Hills brought out darker tones, even in their most wittily dazzling numbers. In their fleeting liaisons in New York, Ms. Quiroga has been the Fonteyn to his Nureyev, the gorgeous monarch finding new sparkle from the exuberance of a younger consort.

Ms. Espinoza is discreetly glamorous, youthful, elegant, with wide, dark eyes; a first impression is that she brings out his tenderly romantic side. The two dances they performed in the confined space of a ground-floor room at the consulate had only a few of the thunderbolts that he loves to hurl (from the knee down). A rapidly trilling diagonal path on his heels (ankles crossed) won applause from the audience, seated on all four sides. But the central experience was one of pure tango style, deeply sensuous, all the more moving when observed at close quarters. It’s now become a cliché to call him “the Baryshnikov of tango,” but it’s still justified when you reflect that Mikhail Baryshnikov’s dancing was founded, above all, in beauty even more than in brilliance.

Though much of Mr. Missé’s magic comes from his feet and his phrasing, a touchstone of his style comes from the high, gentle placing of his right hand on his partner’s back. Ms. Espinoza wore a black calf-length dress (the bodice decorated with white embroidery) which exposed most of her back; Mr. Missé touched one or the other of her shoulder blades with wonderful delicacy.

Their second number — to the song “Soñemos,” recorded by Carlos di Sarli — was an ideal demonstration of the give-and-take of partnering at its most intimate. No high extensions, no lifts. At times, Ms. Espinoza turned him (his feet interlocked, with one resting needlelike on the toe); elsewhere, their feet circled around each other or made darting invasions. With each, it was a pleasure to watch the dovetailing of crossed ankles. Mr. Missé remains a master of playfulness: Once, he simply let go of Ms. Espinoza, showing her perfect equilibrium for a marvelous moment; at another moment, he not only let go but also did a single turn before returning to their tango embrace.

They moved together in smoothly pouncing steps that flowed in long, thick-cream phrases; their brows touched almost nonstop, as if locked in shared thought. Especially touching were their sudden pauses: not stops, but moments of suspense. This is the kind of dancing that makes you cry without being able to explain why; to be near it is to share its luxury.