Marques started out in karting, proving his ability by winning both regional and national titles. Following his apprenticeship in karting, he contested the nationally-based Formula Chevrolet series - the equivalent of Formula Opel in Europe - in 1992.
He proved to be among the most talented individuals on show, and eventually took the title ahead of future Indycar stars Tony Kanaan and Helio Castroneves.
Marques made a good impression when he stepped up to the 1993 SudAm Formula 3 series with a Ralt-Mugen Honda.
The ambitious Brazilian youngster headed to Europe to contest the F3000 championship the following season and garnered a fourth place at Magny Cours. A move to a seat in the crack DAMS team for 1995 put the fast but sometimes wayward Tarso in contention for F3000 championship honours, but he eventually had to settle for fifth in the standings with a win at Estoril to his credit.
A chance to shine in Grands Prix came early in 1996 when Marques was entrusted with the Minardi for the two South American races. Although he immediately impressed, the Brazilian was consigned to a testing role with Bridgestone until a recall to the ranks came in mid-1997 when Trulli left to drive for Prost.
Unfortunately, nothing startling was achieved in the tail-end car and Marques was left without a drive of any sort for 1998.
However, a fabulous test for the Payton-Coyne team was to alert the CART community to the Brazilian's undoubted speed, and he was given six races by Penske in 1999. The car's uncompetitiveness hampered Tarso's chances of making a big impact.
In November 2005 it was rumored that he had raised enough money to become Midland F1's third driver as Nicky Pastorelli ran out of funds. As it turned out, neither driver gained the necessary sponsorship to compete for Midland as there was fierce competition for the role, with Midland being the only team left in Formula One regularly employing pay-drivers.