Schrader began racing at Lake Hill Speedway in Valley Park in 1971 and graduated quickly to sprint cars around the Midwest. In USAC competition he won four sprint car races, six Silver Crown races, and 21 midget races under USAC sanction, establishing a reputation for adaptability across car types. He attempted to qualify for the 1983 Indianapolis 500 but wrecked during practice. His NASCAR debut came in 1984 when he leased a Ford to compete at Nashville, finishing nineteenth in his first start. He ran four more races that season and won the 1985 Winston Cup rookie of the year award while driving the No. 90 Ford for Junie Donlavey.
In 1988 Schrader joined Hendrick Motorsports in the No. 25 Folgers-sponsored Chevrolet, listed under team patriarch "Papa Joe" Hendrick. He immediately made an impact, winning the Daytona 500 pole — the first of three consecutive years he claimed that particular pole — and earning his maiden Cup victory at the Talladega DieHard 500. A second win followed in 1989 at Charlotte Motor Speedway, and he posted fifth-place finishes in points in both years. His third career victory came in 1991 at the Motorcraft Quality Parts 500, followed shortly by a fourth at Dover International Speedway, which proved to be his final Cup win. That year he recorded nine top-five finishes and placed ninth in points.
His career-best points result came in 1994 when he finished fourth in the championship. He also earned a career-high six poles in 1993. In 1995, a mishap in a NASCAR Supertrucks practice session at Evergreen Speedway cost Schrader the top of his left thumb. After nine seasons with Hendrick, he departed following a twelfth-place points finish in 1996.
Schrader moved to Andy Petree Racing in 1997 driving the No. 33 Skoal Bandit Chevrolet, finishing tenth in points — his final top-ten championship result. He continued competitive if unspectacular NASCAR seasons through MB2 Motorsports, BAM Racing, and Wood Brothers Racing. At MB2, he was on track at Daytona in 2001 when Dale Earnhardt suffered his fatal crash on the final lap of the Daytona 500. Schrader was one of the first to reach Earnhardt's car and his visibly shaken post-race television interview was among the first signals to the public that something was gravely wrong with the seven-time champion. In a 2011 interview, Schrader acknowledged he had known Earnhardt was dead but chose not to be the one to announce it.
His final two Cup top-ten finishes came during a 2006 season with Wood Brothers Racing. He competed sporadically in the series into the late 2000s before formally announcing his retirement from NASCAR at the end of 2013, describing it less as retirement and more as the absence of plans to return.
Throughout the 1990s and into the 2000s, Schrader built a reputation unique in NASCAR for his willingness — and enthusiasm — to race anything, anywhere. He commonly logged close to 100 starts in a calendar year, mixing Cup and Busch Series events with ARCA, dirt modified, and dirt late model races. He owns Federated Auto Parts Raceway (formerly I-55 Raceway) in Pevely, Missouri, and co-owns Macon Speedway in Illinois alongside Kenny Wallace, Tony Stewart, and promoter Bob Sargent.
In 2013 he became the oldest ARCA race winner and set a NASCAR record as the oldest pole winner in any NASCAR series at age 58, claiming the pole for the inaugural Mudsummer Classic at Eldora Speedway in the Camping World Truck Series. He competed in the Superstar Racing Experience in 2022, finishing third at his own track. In August 2023, racing in the NASCAR Pinty's Series in Canada, he won the Freshstone Dirt Classic at Ohsweken Speedway at the age of 68, becoming both the first non-Canadian to win in the series and the oldest driver ever to win a NASCAR-sanctioned event.
Schrader was inducted into the St. Louis Sports Hall of Fame in 2024. His career is defined less by championship titles — he never won a Cup championship — than by an extraordinary breadth of competition and an enduring love of racing in virtually every form. He is a first cousin once removed of fellow NASCAR driver Carl Edwards.