Narayanaswamy's major break came at a
Madras Music Academy concert in 1951, when he was unexpectedly forced to substitute for his guru,
Ariyakudi Ramanuja Iyengar who was not in a position to attend the conference under unforeseen circumstances. Accompanied by doyens
Palghat Mani Iyer and
Papa Venkataramayya, this concert proved to be a milestone in Narayanaswamy's career. The training under
Palghat Mani Iyer allowed Narayanaswamy to develop a solid knowledge of rhythmic nuances. This in turn would enable him to be at ease in the company of such legends of percussion as
Palani Subramaniam Pillai,
Palghat R. Raghu,
Mavelikkara Velukkutty Nair, and
Umayalpuram K. Sivaraman to name a few. Narayanaswamy,
Palghat R. Raghu, and violin maestro
T.N.Krishnan soon became a frequent and much admired combination on stage. K.V.Narayanaswamy was intimately connected to the
Travancore royal family following his skilful rendition of
Swathi Thirunal Rama Varma's
Navaratri compositions. Another landmark in Narayanaswamy's life came in 1964 when he participated in the
East-West Encounter concerts in New Delhi. This was followed by a widely acclaimed concert at the
Edinburgh Festival in Scotland in 1965. On being made professor of music at
Wesleyan University,
Middletown, Connecticut, between 1965 and 1967, he went on a
coast-to-coast concert tour of US. He was one of four artists including
Bismillah Khan,
Ali Akbar Khan, and
Ravi Shankar who participated in the hugely popular
Hollywood Bowl music festival in Los Angeles in the summer of 1967.In 1974, Narayanaswamy went to teach in
Berkeley, California for a year, in the company of dancer
Balasaraswati and sitarist
Nikhil Banerjee. Invited by the
American Society of Eastern Arts, he travelled to North America, Europe (Berlin Music Festival in 1976) and Australia (Adelaide Arts Festival in 1988) multiple times thereafter on various concert tours. He also joined the Music College in
Madras as a lecturer in 1962 when
Musiri Subramania Iyer was its principal, and retired as Professor of Music in 1982.In 1984, Narayanaswamy was to become the first Indian musician to be awarded the
Fulbright Scholarship and went to
San Diego State University in California as an artist-in-residence under the scholarship. For nine months he taught at the university and gave performances all over North America. ==Musical style and song repertoire==