They may be separated by several centuries and thousands of miles, but American jazz tap and the classical Indian Kathak tradition are driven by the same irresistible impulse — to create rhythmically inventive “music’’ with the feet.

INDIA JAZZ SUITES: Kathak Meets Tap World Music/CRASHarts

At: the Institute of Contemporary Art, last night (through Sunday)

In the provocative “India Jazz Suites: Kathak Meets Tap,’’ presented by World Music/CRASHarts last night at the Institute of Contemporary Art, veteran Kathak dancer Pandit Chitresh Das and Emmy Award-winning choreographer/dancer Jason Samuels Smith, 29, renowned for his explosive tap work in Broadway’s “Bring in ’Da Noise, Bring in ’Da Funk,’’ offered a dynamic exchange of dance ideas that brilliantly illuminated distinctive differences and surprising commonalities between their respective art forms, electrifying an enthusiastic sold-out crowd. Both dancers were charmingly affable, chatting up the audience with anecdotes, jokes, and explanations.

Individual solo sets showcased each dancer’s stylistic strengths, each fueled by a superb trio of musicians. The innovative Smith, as he rapped at one point, speaks “right through the toes and the heels,’’ from crisp, delicately articulate cascades of taps to the powerful pounding of a pile driver. He is a dazzling technician, his feet carrying his body through flamboyant kicks, glides, scrapes, skitters, and spins, his body elegantly upright like an old-time hoofer or hunched over, body off-center, legs corkscrewing into turns.

In Das’s art form, the predominant rhythms unfurl through bare feet, complemented by jingly bell cuffs around each calf. But the storytelling is in Das’s expressive face and his intricate, stylized gestures — arms that swirl and slice and fingers that flutter and curl in a kind of sign-language mime. His footwork evokes the power and speed of the warrior or the mincing, quivering steps of a frightened maiden, He and his trio stopped and started complex rhythmic passages with breathtaking precision, and he displayed remarkable multitasking as he danced and sang a song his father taught him while playing on tabla.

Then the mix-up began, with each dancer trading phrases with the other’s musical trio. Das incorporated some of the jazz combo’s syncopations. Smith led the Indian trio into intimations of a funk groove and improvised a dynamite exchange with tabla player Abhijit Banerjee, who picked up the vivid timbral changes in Smith’s feet and added colorful flourishes. Smith and Das did their own solo trading. But rather than merely imitating each other’s style, each seemed to inspire the other to discover new facets of his own art form. Instead of appropriation or fusion, it was a lively cross-cultural rejuvenation that brought the crowd to its feet.