Roberts was born in Daytona Beach, Florida, and raised in Apopka, Florida. He was a pitcher for the Zellwood Mud Hens, an American Legion baseball team, where his fastball earned him the nickname "Fireball" — a moniker that stuck through the rest of his life and racing career. He enlisted with the United States Army Air Corps in 1945 but was discharged after basic training due to asthma, a condition that would prove fatally significant years later.
Roberts attended the University of Florida and raced on dirt tracks on weekends. In 1947, at eighteen, he raced on the Daytona Beach Road Course for the first time, and the following year won a 150-mile race there. He competed in local stock and modified races at Florida tracks including Seminole Speedway before establishing himself in the NASCAR Grand National Series.
Roberts amassed victories despite NASCAR's transition away from shorter dirt tracks to superspeedways in the 1950s and 1960s — a shift that suited his skill set on fast, high-banked circuits. In 206 career Grand National races he won 33 times and earned 32 poles, finishing in the top five 45 percent of the time and in the top ten 59 percent of the time. He won his first Southern 500 in 1958, driving a Chevrolet prepared by Paul McDuffie.
His most celebrated season came in 1962, when he won both the Daytona 500 and the Firecracker 250, driving a black and gold Pontiac built by the legendary fabricator Smokey Yunick. That same year he achieved a class win at the 24 Hours of Le Mans driving a Ferrari 250 GTO entered by the North American Racing Team, demonstrating versatility that extended beyond American oval racing. He also designed Augusta International Raceway, where he would record his final victory.
In 1961, Roberts served as temporary president of the Federation of Professional Athletes, a Teamsters-affiliated drivers' union that he and Curtis Turner had helped organize in opposition to NASCAR president Bill France, who moved aggressively to disband it. Unlike Turner and Tim Flock, who received life bans for their union roles, Roberts soon returned to the NASCAR fold.
On May 24, 1964, at the World 600 in Charlotte, Roberts was caught up in a seven-car accident on lap seven when Ned Jarrett and Junior Johnson collided. Roberts' Ford slammed backward into the inside retaining wall, flipped, and burst into flames. Jarrett rushed back to pull him from the car. Roberts suffered second- and third-degree burns over 80 percent of his body and was airlifted to hospital in critical condition. His condition worsened over the following weeks: he contracted pneumonia and sepsis, slipped into a coma, and died on July 2, 1964 — forty days after the crash. His concealed asthma was believed to have made the fire-retardant chemicals used in his treatment additionally dangerous to his breathing.
Roberts' death, coinciding with the deaths of Eddie Sachs and Dave MacDonald at the Indianapolis 500 just six days after his crash, galvanised the racing world around fire safety. The aftermath directly produced the Firestone RaceSafe fuel cell, mandatory Nomex racing suits, and the five-point safety harness and contoured driver's seat as universal NASCAR requirements. Modern motorsport's fire-safety infrastructure owes a significant debt to the public pressure generated by Roberts' prolonged and publicised death.
Despite the championship gap in his record, Roberts was posthumously named one of NASCAR's 50 Greatest Drivers. He was inducted into the International Motorsports Hall of Fame in 1990, the Motorsports Hall of Fame of America in 1995, and the NASCAR Hall of Fame in 2014. The city of Concord, North Carolina, named a street near Charlotte Motor Speedway in his honour in 2000. The Fireball Run, a charitable team competition launched in 2007, carries his name as a tribute.