Sospiri began racing in the Italian 100cc karting championship at the age of fifteen in 1981. His karting career was described by Michael Schumacher as "dominating": he won multiple Italian and European karting championships before claiming the 100cc World Karting Championship in 1987.
After progressing through Formula Ford from 1988, Sospiri reached Formula 3000 in 1991 as teammate to Damon Hill in the Middlebridge Lola T91/50 Cosworth. The car was uncompetitive and he scored nine points across the season, including a second place at the German round at Hockenheimring. A step back to the Italian F3 series followed in 1992 before he returned to Formula 3000 in 1993, driving a Reynard 93D Judd for Mythos. He moved to Super Nova for 1994 and mounted a championship challenge without winning, finishing fourth. In 1995 he won three races and beat teammate Ricardo Rosset to the Formula 3000 title.
Despite winning the Formula 3000 championship in 1995, few Formula One options materialised and Sospiri spent 1996 as Benetton's official test driver. He had previously tested for Simtek at Estoril in 1994 but could not raise the funds for a race seat at that time.
His only Formula One race appearances came with the MasterCard Lola project in 1997. At the opening race, alongside former F3000 teammate Rosset, both drivers were more than ten seconds off the pace and failed to qualify under the 107% rule. The team withdrew from the championship before the Brazilian Grand Prix due to massive debts, bringing Sospiri's F1 career to an abrupt end after a single failed qualifying attempt.
After the Lola collapse, Sospiri joined Team Scandia for the 1997 Indianapolis 500. He qualified third on the grid — a remarkable debut — and finished seventeenth. Later in that season he recorded a second-place finish at New Hampshire Motor Speedway. He completed six of ten races in the 1996-97 season, finishing 21st in the championship.
In 1998, Dan Gurney's All American Racers brought Sospiri in as a late-season replacement for P.J. Jones for the final four races. He recorded best finishes of 15th at Houston and Surfers Paradise. An entry for the 1999 Indianapolis 500 under ISM Racing ultimately went to Brian Tyler, who failed to qualify.
Sospiri won the Sports Racing World Cup in both 1998 and 1999, co-driving a Ferrari 333 SP with Emmanuel Collard. That form earned a works Toyota drive at the 1999 24 Hours of Le Mans alongside Collard and Martin Brundle. The polesitting Toyota suffered persistent gearbox problems and a puncture while Brundle was driving, ending its race.
Sospiri retired from racing in 2001 and became team manager of Vincenzo Sospiri Racing, the team he founded.
Michael Schumacher ranked Sospiri as his first racing hero, ahead of Ayrton Senna, crediting him as a karting inspiration. Sospiri's own list of heroes included Senna and Dan Gurney. The MasterCard Lola failure of 1997 is remembered as one of Formula One's most dramatic team collapses; Sospiri's near-certain future in top-level racing was cut short by circumstances largely beyond his control. His standout 1997 Indianapolis 500 qualifying performance — third on the grid in his IndyCar debut — demonstrated the raw speed that made him a respected figure across disciplines.