Gugelmin grew up in Joinville in a wealthy family and began kart racing at the age of seven in 1971, winning his local championship nine consecutive years through 1979 and the Brazilian national karting title in 1980. He then won the Brazilian Formula Fiat Championship in 1981 before following the path of many Brazilian drivers to the United Kingdom in 1982.
In Britain, Gugelmin shared a house with Ayrton Senna from 1982 to 1987. Senna used his connections with the Van Diemen team to secure Gugelmin a drive in British Formula Ford 1600, which Gugelmin won outright in 1982 with 13 victories. He was runner-up in British Formula Ford 2000 in 1983, then won the European Formula Ford title in 1984. In 1985, driving for West Surrey Racing in British Formula Three, he won both the championship and the season-ending Macau Grand Prix — emulating Senna's own Macau victory two years earlier. He spent two further seasons in International Formula 3000, taking one victory at Silverstone in 1987 for the Ralt factory team.
Gugelmin entered Formula One with the March team in 1988, partnering Ivan Capelli in a car designed by Adrian Newey. After five retirements in the first six races, he scored fourth place at the British Grand Prix and fifth at the Hungarian Grand Prix, finishing the year as the highest-scoring newcomer in the championship in 13th place overall.
The 1989 season yielded Gugelmin's sole Formula One podium: third place at the Brazilian Grand Prix, a strong result given March's financial difficulties. At the French Grand Prix that year, he was involved in a spectacular accident at the start — his car performing a dramatic barrel roll — that stopped the race. Gugelmin took the restart from the pit lane, ultimately setting the race's fastest lap, the only one of his F1 career.
In 1990, the March team was sold and renamed Leyton House. The new CG901 chassis proved unreliable; Gugelmin and Capelli failed to qualify six times during the season. A notable exception came at the French Grand Prix, where modifications to the car transformed its performance, and the two drivers ran first and second for much of the race before Gugelmin retired with engine trouble. He salvaged a single championship point that year with sixth at the Belgian Grand Prix.
The 1991 season saw internal turmoil at Leyton House, with team principal Akira Akagi arrested on fraud charges in September. Gugelmin managed only three seventh-place finishes across the year. He moved to Jordan for 1992, but the team's underpowered Yamaha engine and financial instability left him without a points finish in 16 races. He departed at season's end.
Gugelmin joined Dick Simon Racing for the last three races of the 1993 CART season, then moved to Chip Ganassi Racing in 1994, partnering Michael Andretti. He settled into competitive form with PacWest Racing, where he would spend the bulk of his American career alongside British driver Mark Blundell.
His best CART season came in 1997, when a fitness programme — he shed 40 lb (18 kg) — combined with a switch to Firestone tyres and Mercedes-Benz engines elevated PacWest's competitiveness. Gugelmin won his only CART race that year at the Molson Indy Vancouver, a victory celebrated widely across the paddock. He finished fourth in the championship standings that season. At the season-ending California Speedway, Gugelmin set a world closed-circuit speed record of 240.942 mph (387.759 km/h) in qualifying, a record that stood until 2000 when Gil de Ferran surpassed it at the same venue.
At the 1995 Indianapolis 500, Gugelmin led 59 laps before finishing sixth — his best result at the Brickyard across multiple attempts.
The 2001 season brought tragedy and danger. During practice at Texas Motor Speedway, Gugelmin crashed heavily, registering impacts of 66.2 g and 113.1 g. The event was eventually cancelled after drivers reported dizziness and nausea from the banked oval's extreme forces. In the week before the Nazareth Speedway race, Gugelmin's son Giuliano — who had been quadriplegic from birth due to cerebral palsy complications — died at the age of six. Gugelmin did not compete at Nazareth, and PacWest withdrew his entry as a mark of respect. He retired from racing at the end of 2001.
Across 147 CART starts, Gugelmin achieved eight podiums and one victory. In Formula One he collected 69 points and competed in 74 Grands Prix. Following retirement, he returned to Brazil to run the family timber business alongside his brother Alceu, and conducted consultancy work for Mercedes-AMG. His friendship and parallel career trajectory with Senna made him one of the most recognizable figures from the Brazilian wave that transformed Formula One in the 1980s.