Vasser won the 1986 Formula Ford National Championship in the SCCA. He competed in the 1988 Corvette Challenge, then in the 1989 and 1990 Pro F-2000 Canadian Championship alongside teammate Ken Murillo under Lucasfilm sponsorship. In the Atlantic Championship in 1990 and 1991 with Genoa Racing / Della Penna Motorsports, he won the Formula Atlantic East/West Challenge in 1990 and finished runner-up in 1991 — four points behind Jovy Marcelo — with six wins and seven pole positions.
Vasser made his CART debut in 1992 and qualified for the Indianapolis 500 as the fastest rookie qualifier that year. In 1995 he joined Chip Ganassi Racing. At that year's Indianapolis 500 he was battling for the lead when he crashed with thirty laps remaining. Later that season, he was initially elevated to victory at Portland after race winner Al Unser Jr. failed post-race inspection for insufficient ground clearance; following a protest and appeals process, Unser was reinstated as winner in September. Vasser finished eighth in points in 1995.
In 1996, Vasser won the CART season opener at Homestead — officially his first win in Indy/Champ Car — and won four races total, including the U.S. 500 at Michigan. He built a large points lead through the first half of the season with seven top-tens in seven races, and clinched the championship at the season finale, scoring points in every race but one.
Vasser finished third in points in 1997 with one win, and second in points in 1998 with three wins including the Marlboro 500 at Fontana. In both seasons teammate Alex Zanardi outshone him and won the championship. In 1999, paired with teammate Juan Pablo Montoya, Vasser was again outperformed: Montoya won the championship in his rookie season. In 2000, his final year with Chip Ganassi, Vasser won the Houston Grand Prix for his first victory since 1998. That year Ganassi became the first major CART team to crossover to the IRL and compete at Indianapolis; Vasser led five laps there but finished seventh. Montoya dominated and won the race.
For 2001, Vasser moved to Patrick Racing in the No. 40 Reynard Toyota and started the season with four consecutive finishes between fourth and sixth. He also rejoined Target Chip Ganassi Racing for the Indianapolis 500, where he finished fourth as CART drivers swept the top five. Back-to-back crashes at Milwaukee and Detroit then derailed the season, and Vasser managed only four further top-seven finishes in the remaining sixteen races.
In 2002, Vasser drove the No. 8 Shell Lola Ford for Rahal Letterman Racing. He scored pole and second place at Long Beach behind Michael Andretti, then closed the year strong with points in each of the final nine races, including a podium at Miami and a dominant win at Fontana after a late-race pass of Andretti. That Fontana victory averaged 197.995 mph (318.642 km/h) — the fastest CART race on record at the time — and was the final win of his CART career.
Without sponsorship at Rahal for 2003, Vasser joined Stefan Johansson's American Spirit team. The team ran the Reynard chassis, which was no longer competitive following Reynard's bankruptcy, with teams forced to absorb their own development work. Outside two fourth-place finishes, fifteen laps led at Cleveland, and a podium at Surfers Paradise in a wet-dry race, the season was difficult, with rookie teammate Ryan Hunter-Reay outpacing Vasser. A return to Rahal Letterman for the Indianapolis 500 ended with another gearbox failure.
In 2004, Vasser became co-owner of PKV Racing (later renamed KV Racing Technology) alongside Dan Pettit and Kevin Kalkhoven and continued driving for the team. He broke the modern CART–Champ Car record for most consecutive starts that year. He retired from open-wheel racing in 2006 but returned briefly to drive in the final Champ Car World Series event at the 2008 Toyota Grand Prix of Long Beach.
In 2006, Vasser competed in three Grand-Am Rolex Sports Car Series races including the 24 Hours of Daytona, driving for GAINSCO/Blackhawk Racing. He returned to that team — renamed GAINSCO/Bob Stallings Racing — for the 2007 Daytona 24 Hours and the season-ending Sunchaser 1000 km. In 2008 he rejoined Stallings at Laguna Seca, paired with fellow Champ Car champion Cristiano da Matta.
As co-owner of KV Racing Technology, Vasser celebrated his most prominent ownership success at the 2013 Indianapolis 500, won by driver Tony Kanaan. He subsequently co-founded Vasser Sullivan Racing, which claimed the GTD Pro teams title at the 2023 IMSA SportsCar Championship.
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