Eubanks was born on August 9, 1925, in Spartanburg, South Carolina. He entered the United States Armed Forces during World War II, serving alongside fellow NASCAR veterans Bud Moore and Cotton Owens — a connection that would link three men who would each go on to significant roles in the sport's early development.
Eubanks began racing in 1950 and competed through 1961 in the NASCAR Grand National Series. Over that span he recorded one race win, 37 top-five finishes, and 81 top-ten finishes. His total career earnings amounted to $35,338, which when adjusted for inflation represents roughly $380,000. He completed 14,303.3 miles of competitive racing over the course of his career.
Dirt tracks were the setting where Eubanks performed most consistently, and top-ten finishes on those surfaces were a reliable part of his results. Superspeedways, by contrast, proved difficult for him; his average finish on those tracks was 38th place, a notable contrast to his dirt-track competitiveness.
As one of the earliest competitors to take part in a NASCAR road racing event, Eubanks finished second at that occasion behind Al Keller, who was driving a 1951 Hudson Hornet. The result was among the more distinctive entries in his statistical record, reflecting the varied formats NASCAR experimented with during the sport's early years.
At the 1955 Southern 500 at Darlington, Eubanks was credited with driving the fastest Oldsmobile 88 in the field, a distinction that reflected both his mechanical familiarity with the car and his ability to extract pace from the machinery at one of the most demanding tracks on the circuit.
Eubanks' primary racing vehicle was the number 88, a Ford machine owned by Don Every and Domenic Petti of Daytona, Florida. The car was a consistent presence in the field during his active years, and the partnership with Every and Petti defined much of the infrastructure behind his career.
In 1960, Eubanks appeared as one of the extras in Thunder in Carolina, a stock car racing film. The production drew on real-life drivers and figures from the NASCAR world to populate its race sequences, and Eubanks' participation reflected his standing as a recognizable name in the sport at the time.
Joe Eubanks died on June 21, 1971. His career represents the profile of a steady mid-field competitor who thrived on the dirt surfaces that dominated early NASCAR but found the transition to superspeedways more difficult. His connection to Bud Moore and Cotton Owens — two men who became major forces in NASCAR as owners and crew chiefs — places him within a tight-knit community of veterans who shaped the sport in its foundational decade.