Rudd was born in South Norfolk, Virginia (now Chesapeake), the son of Alvin R. Rudd Sr., president of Al Rudd Auto Parts. He began racing as a teenager in karting and motocross before making his NASCAR debut at Rockingham in 1975, aged 18, driving a No. 10 Ford for family friend Bill Champion. He went full-time in 1977 and was named Rookie of the Year. By 1979 he had signed with Junie Donlavey and earned four top-five finishes while finishing ninth in the championship standings.
In 1981 Rudd joined DiGard Motorsports, winning three poles and beginning a remarkable consecutive-start streak. The following season he moved to Richard Childress Racing's No. 3 Pontiac, where despite six top-fives he finished ninth in points. At the 1983 Daytona 500, Rudd became the youngest pole winner in that race's history at 26, a record that stood until 2014. He claimed his first two career victories that year at Riverside and Martinsville.
In 1984, Rudd and Dale Earnhardt swapped rides when Earnhardt moved to Childress and Rudd took the No. 15 Ford for Bud Moore Engineering. That year's Busch Clash at Daytona produced one of the most dramatic stories of his career: Rudd suffered a concussion and torn rib cartilage in a crash that left his eyes so swollen he taped them open to compete in the Daytona 500 — wearing a flak jacket to protect his ribs. He won the very next race at Richmond. The incident led NASCAR to institute mandatory medical examinations for drivers involved in crashes before allowing them to race again. Rudd stayed with Bud Moore through 1987, reaching a career-best fifth in the championship in 1986.
After leaving Bud Moore, Rudd drove the No. 26 Buick for Kenny Bernstein's drag-racing-heritage team from 1988, winning at the inaugural Sears Point road course event in 1989. In 1990 he joined Hendrick Motorsports in the No. 5 Chevrolet and won at Watkins Glen. That season was also marred by a fatal accident in which his car spun into Bill Elliott's pit lane at Atlanta, striking tire changer Mike Rich, who died in surgery. The incident was the direct catalyst for NASCAR introducing pit road speed limits at all tracks.
Rudd finished a career-best second in the championship standings in 1991, a season further marked by controversy at Sonoma, where he was shown the black flag and had an apparent win taken away and awarded to Davey Allison following contact in the closing laps. In 1992 he won at Dover before leaving Hendrick to form his own operation.
Rudd established Rudd Performance Motorsports in 1994, driving the No. 10 Ford Thunderbird with Tide sponsorship. He won at New Hampshire in his first year as an owner-driver and finished fifth in points. His consecutive winning-season streak came under threat multiple times: in 1995 he won only at Phoenix with two races left in the season; in 1996 he survived with a late win at Rockingham. In 1997 he posted two victories including the Brickyard 400 at Indianapolis, his highest single-season win count since 1987. His final win in the streak came at Martinsville in 1998, where he was so badly affected by heat and a faulty cooling system that he gave his victory lane interview lying on the ground, breathing from an oxygen mask. When Tide departed, he closed his team.
Rudd joined Robert Yates Racing in the No. 28 Texaco-Havoline Ford in 2000 and finished fifth in the points standings. He won twice in 2001 at Pocono and Richmond, and scored his final career win at Sonoma in 2002. After two seasons with Wood Brothers Racing and a partial 2006, Rudd retired following the 2007 season.
He ended his career as NASCAR's "Ironman," holder of the record for most consecutive starts at 788. That mark stood until Jeff Gordon surpassed it in 2015.
Rudd's sixteen consecutive winning seasons remains a record tied only by Jimmie Johnson. His career total of 23 wins across 32 seasons, his owner-driver chapter with Rudd Performance Motorsports, and his role in prompting both mandatory medical checks and pit road speed limits represent a lasting imprint on how NASCAR's safety and competition rules developed. He was inducted into the NASCAR Hall of Fame in 2025 and the Virginia Sports Hall of Fame in 2007.