His greatest source of success was in various forms of sports cars, winning four IMSA GTP titles (1988–1991) when racing for Nissan, and one Can-Am championship (1981).

Brabham also won the 1993 24 Hours of Le Mans driving one of the factory Peugeot 905 alongside French drivers Éric Hélary and Christophe Bouchut.

Geoff Brabham became just the third Australian driver to win Le Mans after Bernard Rubin (1928) and Vern Schuppan in 1983.

The pair initially finished second behind BMW Motorsport Australia teammates Paul Morris and Craig Baird, but a blunder by the team left Baird in his car at the final pit stop which meant that by the end of the race, the Kiwi driver had breached the race regulation which limited any one driver to a maximum of three hours continuous driving.

After a successful karting career, Matthew moved into international open-wheel racing and the Road to Indy ladder; he is also a three-time Stadium Super Trucks champion.