Welborn was born in Denton, North Carolina and came of age during the early years of organized stock car racing in the American South. His career coincided with the formative period of NASCAR, when the sport was establishing its structures, venues, and rules. He became closely associated with car owner Julian Petty, with whom he drove for a substantial portion of his career.
Welborn made his Grand National Series debut in 1953, competing in 11 events for owners Julian Petty and J.O. Goode. He collected two top-five finishes and six top-ten results in that opening campaign, establishing himself as a reliable mid-field competitor.
In 1954, he drove in nine events for a trio of owners — Julian Petty, Bob Griffin, and George Hutchens — adding one top-five and three top-ten finishes. His progression continued in 1955, when he drove in 32 of 45 events for Julian Petty's operation, claimed the pole at Greenville-Pickens Speedway, and finished fourth in the overall points standings.
The 1956 season brought Welborn his first championship, as he captured the NASCAR Convertible Division title while also competing in six Grand National events. He repeated as Convertible champion in 1957, a year in which he also recorded his first Grand National victory at Martinsville — though the circumstances were unusual. Welborn left the race halfway through due to illness and was relieved by Lewis "Possum" Jones, yet NASCAR credited the win to Welborn as the starting driver, following the established rule of crediting the driver who began the race. He recorded one win, one pole, and three top-ten finishes in five Grand National starts that year.
The 1958 season was Welborn's most dominant. He won four consecutive races — five in total — during the year while competing in 18 of 51 events, all for Julian Petty. He also added ten top-five and 15 top-ten finishes and claimed his third consecutive Convertible Division title. Despite these accomplishments, his limited schedule meant he finished only 149th in Grand National points for the year.
Welborn carried his momentum into 1959, when he won the pole position for the inaugural Daytona 500 by claiming his qualifying race in a car prepared by Paul McDuffie. That season he posted five poles and three wins. His Grand National career wound down in subsequent years, and he made his final NASCAR start in 1964, driving for the renowned Holman-Moody team.
Over his career, Welborn accumulated nine Grand National victories across the 1950s and into the early 1960s, making him one of the more successful drivers of that era who competed on a partial schedule.
The NASCAR Convertible Division ran as a parallel series to the Grand National from 1956 to 1959 and used the same tracks and events, with the distinction that competitors drove open-top production cars. Welborn dominated the division's final three seasons — 1956, 1957, and 1958 — winning all three championships before the series was discontinued after the 1959 season. His dominance in the Convertible Division ran alongside a strong Grand National presence and helped define his legacy as a complete competitor of the era.
Welborn was inducted into the National Motorsports Press Association's Hall of Fame in 1982, recognizing his contributions to American stock car racing over more than a decade of competition. In 1998, one year after his death, he was named to NASCAR's 50 Greatest Drivers list, a selection that honored the most accomplished and influential figures in the sport's history up to that point. The recognition placed him alongside contemporaries such as Lee Petty, Buck Baker, and Herb Thomas, who had similarly shaped NASCAR's foundational era.