Allen began karting at the age of five in Raleigh, North Carolina, and progressed steadily through the ranks. By sixteen he had won several World Karting Association Championships and had moved on to dirt late model cars. He also pursued aviation alongside his motorsport ambitions, earning a commercial pilot's licence from Embry-Riddle Aeronautical University.
Allen made his Winston Cup debut at Daytona International Speedway on July 3, 1993, driving the No. 37 Naturally Fresh Ford — a former Robert Yates race car — and finished 29th after starting 40th. He also ran at Talladega Superspeedway that year, placing 26th, before joining TriStar Motorsports for the race at Phoenix Raceway in October.
In 1994 Allen drove the No. 19 Hooters Ford for TriStar Motorsports. He had already won eight poles in fifteen ARCA Series starts that off-season, including a race at Atlanta Motor Speedway. At the season-opening Daytona 500 he set the fastest qualifying time, becoming the first rookie in Winston Cup history to win the Daytona 500 pole; he was 27 years old, making him the second-youngest Daytona 500 pole winner behind Ricky Rudd, who had taken the honour at 26 in 1983. Allen went on to finish 22nd in the race. His 1994 season included a seventh-place finish at the Coca-Cola 600 in Charlotte, and he claimed three poles overall — at Daytona, Atlanta, and Michigan — though he failed to qualify for twelve races and finished 39th in the championship standings with seven DNFs.
For 1995 Allen joined Junior Johnson's team driving the No. 27 Hooters Ford. He finished 17th at Daytona and 18th at Darlington, but failed to qualify at Atlanta — where he had been on pole the previous year — and was replaced by Hut Stricklin at Bristol. He subsequently returned to TriStar Motorsports, attempting nine races and qualifying for seven. At Talladega he qualified second and achieved his career-best Winston Cup finish of tenth. He also attempted Indianapolis and Michigan for Sadler Brothers Racing but missed both races.
In 1996 Allen suffered a neck injury in the second race of the season at Rockingham Speedway, sidelining him for several races. He recovered and returned for events at Pocono and Talladega. He continued with TriStar Motorsports in 1997, running at Daytona and Rockingham. After a two-year break he returned in 1999 to qualify for races at Michigan and Daytona.
Allen made four Busch Series starts over his career, with a career-best seventh-place finish at Talladega Superspeedway in 1998, driving the No. 78 Church's Chicken Chevrolet. His other Busch starts came at Charlotte in 1995 and at California in 1997.
Allen was competitive in the ARCA Series prior to his 1994 Winston Cup season, winning a race at Atlanta Motor Speedway and claiming eight poles in fifteen starts, which helped establish his credentials ahead of the Daytona pole effort.
After his motorsport career, Allen moved into real estate development. His commercial pilot's licence, earned at Embry-Riddle, remained a professional qualification he held alongside his racing identity.