Kristensen's competitive career began in karting in 1984. He won the 1985 Nordic Formula A series, defeating a field that included future Formula One World Champion Mika Häkkinen. After his first open-wheel outings in Formula Ford in 1987 and a German Formula Three debut at Brno in 1989, Kristensen paused racing to complete training as a bank clerk before returning full-time in 1991. Given a seat in German Formula Three by Bertram Schäfer, he won the opening race at Zolder from pole and claimed seven further podiums over the season, securing the championship title.
From 1992 Kristensen relocated to Japan, competing in Japanese Formula Three and the Japanese Touring Car Championship simultaneously. He won the 1993 Japanese Formula Three title with the TOM'S outfit and ran consistently at the front of the JTCC, finishing second in the standings in both 1993 and 1994, on the latter occasion losing the title to Masanori Sekiya by a single point. In 1995 he claimed his maiden Japanese Formula 3000 win at the Mine Circuit.
Returning to Europe for the 1996 and 1997 International F3000 seasons, Kristensen raced for Shannon Racing and Auto Sport Racing respectively, recording a second place at Silverstone in 1996 and inheriting victory at the opening 1997 round at Silverstone after Ricardo Zonta's disqualification.
Kristensen's Le Mans story began with an extraordinary debut in 1997. Called in as a late substitute by the Joest Racing Porsche team just two days before the race after Davy Jones was injured, he partnered Michele Alboreto and Stefan Johansson in a Porsche WSC-95 with barely 20 practice laps completed. Kristensen drove a sequence of fastest laps during the night, turning an intended triple stint into a quadruple stint, and the crew won the race by one lap after a fire eliminated the leading factory Porsche 911 GT1.
After two Le Mans campaigns with BMW in 1998 and 1999 — the second of which ended in heartbreak when teammate JJ Lehto crashed while leading in the closing hours — Kristensen joined the Joest-run Audi factory effort. With Emanuele Pirro and Frank Biela, he won the 2000, 2001, and 2002 editions of the 24 Hours consecutively, the trio becoming the first drivers ever to share three straight Le Mans victories. The 2001 win was achieved in treacherous rain with the aid of Audi's Fuel Stratified Injection system.
In 2003 Kristensen temporarily joined Bentley, taking pole position and winning alongside Rinaldo Capello and Guy Smith in the Bentley Speed 8, finishing two laps clear of the sister car. Back with Audi in 2004, Kristensen equalled Jacky Ickx's record of six Le Mans wins, then broke it in 2005, cruising to a seventh victory with a two-lap advantage alongside Lehto and Marco Werner — his sixth consecutive win, a record sequence in the race's history.
After a third place in 2006 and a retirement in 2007 following a wheel failure while leading, Kristensen and Audi returned to the top in 2008, defeating Peugeot in the closing stages with Capello and Allan McNish. A ninth and final Le Mans triumph came in 2013, driving alongside McNish and Loïc Duval; Kristensen dedicated the win to Allan Simonsen, who had died in an accident on the opening lap of that race.
Parallel to his Le Mans record, Kristensen accumulated six wins at the 12 Hours of Sebring. He won the event for the first time in 1999, co-driving a BMW V12 LMR alongside Jörg Müller and JJ Lehto, then added further Sebring victories in 2000, 2005, 2006, 2009, and 2012, the last of which made him the most successful driver in the event's history.
In American Le Mans Series competition between 2001 and 2003, Kristensen won the drivers' championship in 2002 with Capello, triumphing in their No. 2 Audi Sport North America car through strategic victories at Road America, Trois-Rivières, and the season-ending Petit Le Mans.
From 2012, Kristensen competed in the newly formed FIA World Endurance Championship. He and his Audi teammates McNish and Capello won the first WEC race at Sebring, and in 2013 he clinched the drivers' title alongside McNish and Duval — their final season together.
Between 2004 and 2009, Kristensen also competed in the Deutsche Tourenwagen Masters with Abt Sportsline. He claimed his maiden DTM victory at Oschersleben in 2004 and finished third in the championship in 2006, his best DTM season, which included a win from pole at Oschersleben and another victory at Zandvoort. A severe accident at the 2007 season opener at Hockenheim following contact with Alexandre Prémat sidelined him for three rounds and took two years for all after-effects to fully disappear.
Kristensen retired from professional motorsport on 19 November 2014, announced at a press conference in Copenhagen, closing a career defined by extraordinary endurance, consistency, and speed across multiple disciplines. In August 2014, Queen Margrethe II of Denmark appointed him a Knight of the Order of the Dannebrog. In January 2018 he was inducted into the Danish Sports Hall of Fame. He is widely considered the greatest driver in the history of the 24 Hours of Le Mans.