Alexander established himself as a dominant short-track racer in the American South before reaching NASCAR's national stage. He was the track champion at Nashville International Raceway — now known as Fairgrounds Speedway — in both 1978 and 1992. In 1983, driving Late Models on paved tracks for car owner Bobby Ray Jones, he won the NASCAR Weekly Racing Series national championship and simultaneously claimed the NASCAR Grand American Stock Car championship in the final year that title was contested. His 31 wins from 56 starts that season were concentrated primarily at Nashville, Tennessee and Birmingham, Alabama, where he also won the track championship, though he competed as far afield as South Carolina and Florida. Alexander came from a Nashville family with deep roots in the automotive business, operating several franchised dealerships in the area.
Alexander's national-level career began in the Winston Cup Series in 1980, when he made the field for the Music City 420 at Nashville and finished tenth. He ran part of the 1981 season for Bob Rogers. In 1984 he attempted most of the first 22 races for car owner Dave Marcis with limited success. He ran a partial 1985 schedule for Sims Brothers and Sadler Brothers before returning in 1988 as substitute for the injured Bobby Allison, driving for the Stavola Brothers in the final sixteen races of that season. The Stavola stint produced his best Cup results: six top-ten finishes in eighteen starts, including a career-best third place at the season finale at Atlanta Motor Speedway. In 1989, Alexander drove the Stavola Brothers car at Daytona but was hindered by an injury suffered in the Snowball Derby at Five Flags Speedway in Pensacola, Florida the previous December and resigned from the ride. His final Cup appearances came in the first seven races of 1990 for Bobby Allison Motorsports.
Alexander ran a partial Busch Series season in 1986, then competed full-time in both 1987 and 1988. He won a race in each of those full-time seasons — at Langley Speedway in 1987 and Hickory Motor Speedway in 1988 — and accumulated three career pole positions. Over 71 Busch starts he recorded 31 top-ten finishes, a strong strike rate that reflected the consistency he had shown on the short tracks earlier in his career.
In 2020, Alexander returned to Fairgrounds Speedway in an involvement with ARCA driver Mason Mingus, who drove a throwback car honouring the Bobby Ray Jones livery from the 1980s. The operation included longtime Fairgrounds member Ben Pruitt and Mark Lawson. A similar arrangement continued into 2021, with Mingus again driving and Alexander directing from above the wall.
Alexander's 1983 NASCAR Weekly Series championship, achieved with a remarkable 31-win season from 56 starts, remains the statistical centrepiece of his career. His national-level work with the Stavola Brothers in 1988 — including the podium at Atlanta — demonstrated competitive capability at Winston Cup level, even if the majority of his career was spent in the shorter-track and regional arena where he first made his name.