Suzuki began in karting, winning the All-Japan Kart Championships in both 1975 and 1976. He translated that foundation into single-seater racing and in 1979 claimed the inaugural All-Japan Formula Three Championship — the first driver ever to win the newly established series.
Through the 1980s Suzuki competed in Japanese Formula Two and Formula 3000 with various teams including Heroes Racing Corporation, Kondou Racing, and Team Le Mans. His breakthrough in the senior domestic formula came in 1995 when he won the Japanese Formula 3000 Championship with Hoshino Racing, succeeding Marco Apicella as champion and preceding Ralf Schumacher in the title lineage. He had also finished runner-up in the 1992 season with Universal Racing.
In 1992 Suzuki reached an early international career high by co-winning the 24 Hours of Daytona alongside Kazuyoshi Hoshino and Masahiro Hasemi. He was a regular participant at Le Mans from 1985 onward, first appearing with the Dome Team on a Dome 85C-Toyota. Early appearances with Dome (1985–86), Team Le Mans and NISMO (1988–90) ended in retirements, though the 1990 outing with NISMO on a Nissan R90CP alongside Hoshino and Hasemi produced a fifth-place finish.
His Le Mans record transformed in 1999. Driving for Toyota Motorsport/Toyota Team Europe alongside Ukyo Katayama and Keiichi Tsuchiya in the Toyota GT-One, Suzuki's car completed 364 laps to finish second overall and take the LMGTP class win — the best result of his Le Mans career. The trio had contested the same event in 1998 in the same Toyota GT-One chassis but retired after 326 laps. Suzuki returned to Le Mans in 2000 with TV Asahi Team Dragon in a Panoz LMP-1 Roadster-S, finishing sixth, and made a final appearance in 2008 for Tokai University/YGK Power in a Courage-Oreca LC70, retiring from that race.
In 1993 Suzuki made two Formula One World Championship starts, standing in for Philippe Alliot at the Larrousse team. Driving the Larrousse LH93 with a Lamborghini V12, he finished 12th at the Japanese Grand Prix and 14th at the Australian Grand Prix, scoring no championship points but completing both races.
Suzuki was a dominant force in the Japanese Touring Car Championship (JTCC) during the early 1990s, winning the 1990 title with Impul in a Nissan Skyline GT-R, finishing first in all six rounds that season. He placed third in 1991 with Impul and again third in 1993 with Nismo, both campaigns also in the Skyline GT-R.
He transferred to the All-Japan Grand Touring Car Championship (JGTC) from 1994, initially with Team Zexel (Nismo) in the Nissan Skyline GT-R GT1 class and finishing third overall in the GT500 standings in both 1995 and 1997. His 1997 season was with Toyota Castrol Team TOM's driving a Toyota Supra in GT500. He continued in the JGTC through 2000 with Toyota Castrol Team TOM's.
In 1996 Suzuki made a single start in the NASCAR Busch Series, driving for Joe Bessey at Nazareth Speedway. An accident during the race left him with a concussion, ending his involvement in American oval racing.
In 2006 Suzuki became director of the R&D Sport team in Super GT, continuing the programme that the Direxiv squad had abandoned. Beyond competition, he worked for Nissan as a test driver, contributing to development of the R35 Nissan GT-R, bridging his extensive on-track experience with manufacturer engineering work.