Smith started his national racing career in the early 1970s, driving his self-built 1969 "Rag Top" Chevrolet Camaro J/Stocker.

Two years later, Smith, along with fellow racer, Rick Hendrick was inducted into the East Coast Drag Racing Hall of Fame.

In 1984, Smith won the prestigious NHRA Summer Nationals held at Old Bridge Township Raceway Park in Englishtown, New Jersey.

In 1990 at Darlington, South Carolina during the IHRA Winter Nationals, Curtis squared off with his father, Earl, in the final round of the event.

From 1990-1995, Smith enjoyed vast amounts of success at Bristol Dragway, winning the IHRA Fall Nationals event four times.

That victory at Darlington, and another later in the year at Maryland International Dragway, propelled Smith to the IHRA Stock Eliminator World Championship at the end of 1996.