Indian Jazz Fusion History
It is impossible to define a starting point for the fusion of Western and Eastern musical styles. Many Western instruments derive from Arabic predecessors, and Arabic music has influenced Western music since Medieval times. More recent Eastern/Western fusion works have their immediate origins in the "Orientalist" period in Western art, beginning in the late 19th century, with the inclusion of Arabic elements in the music of, among others, Debussy and Ravel.
In the 1950's and 1960's, avant-garde artists began to borrow distinctly Indian elements for some of their compositions. LaMonte Young was one such innovator, as was Terry Riley, who studied Northern Indian (Hindustani) vocal techniques with Pandit Pran Nath. Phillip Glass also began to incorporate Indian rhythmic elements in his music around this time.
It was also during this period that jazz artists, in particular John Coltrane, began to draw some of their influence from such elements of Indian music as the raga form (see Edward Strickland's excellent article, What Coltrane Wanted, for more on Coltrane's links to Indian music).
It wasn't until the latter 1960's that classical Indian music found its way into the mainstream of Western music, when the Beatles' George Harrison popularized the sitar. It has since pollinated every imaginable aspect of Western music, including bluegrass, rock and roll, jazz, and (most recently) hip-hop.