In 1983 he came 3rd in the British Formula Three Championship behind Ayrton Senna and Martin Brundle. He also that year tested the Brabham F1 car at Brands Hatch with Bernie Ecclestone, the then team owner, looking at Jones as the next American hope for F1 competition. In the mid-1980s Jones competed in New Zealand Formula Atlantic during the off season and twice won the New Zealand Grand Prix in 1984 and 1987. In 1986 Jones drove for the Factory BMW McLaren Team in IMSA GTP with teammate John Andretti and earned the only BMW GTP victory that season at Watkins Glen. Jones won the 1996 24 Hours of Le Mans with teammates Manuel Reuter and Alexander Wurz in a TWR-Porsche. He also placed second to Buddy Lazier in the 1996 Indianapolis 500, the first of the Indy Racing League era. He has five total starts in the race as well as 16 starts in CART from 1987 to 1996. Jones also made seven Winston Cup starts in 1995 for Jasper Motorsports with a best finish of 20th at Darlington Raceway and participated in the 1992 and 1993 editions of the International Race of Champions finishing 8th and 9th respectively. Jones won the 1990 24 Hours of Daytona driving a Jaguar XJR-12, along with Jan Lammers and Andy Wallace.