Musgrave began racing in 1977 at Waukegan in a 1967 Ford Galaxy inherited from his brother, immediately rebuilding it into a 1967 Ford Torino and winning the track's rookie of the year award. He raced extensively across Wisconsin circuits through the early 1980s, winning features at Capital Speedway (now Madison International Speedway), Wisconsin Dells Speedway, State Park Speedway, and LaCrosse. Notably, in 1980 he finished second in points at Wisconsin International Raceway behind the young Alan Kulwicki. He moved into the ASA series in 1987 driving for Terry Baker, winning at the Milwaukee Mile, Birmingham, and Huntsville and earning ASA rookie of the year honors with a fifth-place points finish.
Musgrave entered Cup competition in 1990, called upon by team owner Ray DeWitt to replace Rich Vogler, who had been killed at Salem Speedway. He made four starts that year and ran the No. 55 for the DeWitt/Ulrich team from 1991 to 1993, finishing runner-up to Bobby Hamilton in the 1991 Rookie of the Year vote and recording twelve top-ten finishes that year. In 1992 he led all Winston Cup drivers in laps completed.
In 1994, Jack Roush signed Musgrave to drive the No. 16 Family Channel Ford Thunderbird as a teammate to Mark Martin. His first season produced three poles and a fifteenth-place points finish. His best Cup season came in 1995 when he had seven top-five finishes, thirteen top-tens, and at one point stood third in the championship standings before slumping late and finishing seventh. He came agonizingly close to a first Cup win multiple times — most notably in 1997 at Darlington, where he ran side-by-side with race leader Dale Jarrett in the closing laps only to be held off. At Pocono the same year he led late before his car went unexpectedly loose and he fell to fourth.
Musgrave was replaced by rookie Kevin Lepage at Roush mid-1998, to widespread surprise. He spent the remainder of that year substituting for various teams and gave Bill Elliott Racing its only top-ten of the season with a fifth at Phoenix. In 1999 he drove the No. 75 Remington Arms Ford for Butch Mock Motorsports but managed only two top-tens before quitting the team. His final regular Cup appearances were with Joe Bessey Motorsports and Team SABCO in 2000. His last Cup start came at Bristol in 2003 when he replaced the suspended Jimmy Spencer.
The Craftsman Truck Series became the arena in which Musgrave's ability was most fully rewarded. He joined Ultra Motorsports full-time in 2001 and immediately won seven races, recording 18 top-ten finishes and finishing second in the championship. He recorded three wins in 2002 and three more in 2003, finishing third in points in both seasons. In 2003 he revealed publicly that he had been battling bladder cancer while racing full-time, a disclosure made more poignant by the fact that his wife Debi had been battling leukemia since 2000.
The 2003 season ended controversially when Musgrave was penalized on the final restart of the season-ending Ford 200 for passing below the restart line, costing him the championship to Travis Kvapil. His post-race reaction — a vow to abandon the rulebook entirely — was never carried out as promised.
Musgrave won the 2005 Craftsman Truck Series championship, his first and only series title, winning one race from the pole at Gateway International Raceway. After Ultra Motorsports closed following the 2005 season, he joined Germain Racing's No. 9 Toyota and continued winning, including a victory at Texas Motor Speedway in 2007 that ended a 66-race winless drought. He was also parked for one race during the 2007 season for deliberately hitting a competitor under caution at the Milwaukee Mile, the first such suspension in Craftsman Truck Series history. He retired from driving in 2012.
Musgrave bridged the gap between Midwest short-track racing and NASCAR's national series over a career lasting more than three decades. His persistence through underfunded Cup rides, near-miss finishes, health challenges, and a controversial championship loss before finally claiming the 2005 Truck title gave his career an arc defined as much by resilience as by results.