Baumgartner made his Formula One race debut at the 2003 Hungarian Grand Prix, substituting for the injured Ralph Firman in the Jordan team; he also took part in the Italian Grand Prix that year.

Plans were made for Baumgartner to drive for Jordan again in 2004 with sponsorship from oil company MOL Rt.

[1] Baumgartner raced throughout the 2004 Formula One season, and after two near-misses (ninth in Monaco and 10th in Canada) he managed to take Minardi's first point in over two years by finishing eighth (classified second last and the last car to take the chequered flag) in the United States Grand Prix held at Indianapolis Motor Speedway.

Baumgartner only participated in a handful of tests for the team and made no race starts.

Prior to the 2008 season, Champ Car unified with the rival IndyCar Series and Stoddart and the Minardi name left the sport.