In 1980 he was awarded second prize in harpsichord improvisation at the Flanders Early Music Festival in Bruges, Belgium, and three years later received third prize for organ playing there. During this period he also taught harpsichord at the Staatliche Hochschule für Musik in Duisburg, Germany (1981-1983). From 1983 he began appearing regularly in Japan as an organ and harpsichord soloist, while serving on the faculty at Kobe Shoin Women's College. He also started conducting small ensembles, an activity that grew over the years, leading to his founding of the Bach Collegium Japan in 1990.
This ensemble, made up of singers and period instrumentalists, began appearing in regular concerts in 1992 with Suzuki as music director. This new activity added to Suzuki's already busy schedule of soloist and teacher: in 1991, he had been appointed professor of organ and harpsichord at the Tokyo National University of Fine Arts and Music, a post he still held in the new century.
Suzuki and his ensemble began recording all of J.S. Bach's cantatas in 1995 for BIS Records, and for the same label he has been recording Bach's complete harpsichord output. In 1999 Suzuki was awarded a Mobil Music Prize in recognition of the general success he has achieved in the performance of Bach's music.