Baldi started competing in rallies in 1972 and turned to racing in 1975 with a Renault 5 in local Italian races. He rose through the ranks and by 1980 had become a top Formula 3 driver, winning the Monaco F3 Grand Prix and going on to win the 1981 European Formula 3 Championship with a record eight victories in a Euroracing Martini sponsored by Marlboro. In 1982 he was signed to drive for Arrows and then moved to Alfa Romeo in 1983 and finished fifth on one occasion at Zandvoort. When Benetton became the Alfa Romeo's team sponsor in 1984 Baldi lost his drive. He went to the underfunded Spirit team in 1984 and 1985. He went on to enjoy a very successful sportscar career with Lancia, Porsche, Sauber and Peugeot, which included winning the 1990 World Sportscar Championship. That same year he did most of the test driving for the Lamborghini F1 project. He won the Le Mans 24 Hours in 1994, sharing a Porsche with Yannick Dalmas and Hurley Haywood.