Carter was born into a motorsport family. His father is IndyCar racer Duane Carter Sr., whose nickname was "Pappy." Carter's own nickname "Pancho" originated before his birth: his father referred to his mother's pregnancy as "little paunch," and the name stuck when he was born, reportedly while his parents were en route to a race at the Milwaukee Mile. Carter is the half-brother of Johnny Parsons, and his full brother Dana Carter also raced in USAC midgets, sprints, and Silver Crown before dying of a heart attack in May 1983. Carter is a graduate of California State University, Long Beach.
Carter launched his national career in midget cars and won the 1972 USAC midget car championship, adding Hut Hundred victories in 1972 and 1975. He accumulated 23 midget car feature wins before leaving the series in 1978.
In sprint cars, Carter was equally formidable, winning the national USAC sprint car championship in 1974 and again in 1976. In doing so, he became the first driver to win both the USAC midget and sprint car championships — a historic double that had not been achieved before him. He ran well on both dirt and pavement, but was particularly dominant on paved high-banked ovals such as Winchester and Salem. On May 30, 1977, he won two USAC midget features and one USAC sprint feature in a single afternoon at Salem Speedway, the day after finishing fifteenth in the Indianapolis 500.
In November 1977, Carter suffered serious injuries in a testing crash at Phoenix International Speedway. The accident left a permanent disability in one of his legs, limiting his effectiveness on road courses for the rest of his career. He returned to competition at the end of March 1978, winning a USAC Sprint race at Indianapolis Raceway Park on Saturday and another at Winchester Speedway the following day — his first races back behind the wheel.
Carter made his Indianapolis 500 debut in 1974, finishing seventh and earning the Rookie of the Year award. He finished third in the 1982 Indianapolis 500 behind the celebrated duel between Gordon Johncock and Rick Mears. His sole Indy Car race victory came at the Michigan 500 in 1981, when he also finished third in the CART championship standings.
Carter's most prominent moment at Indianapolis came in 1985, when he drove a Buick V6-powered car to the pole position for the 1985 Indianapolis 500 — a significant achievement given that the Buick engine was a new and largely unproven powerplant in IndyCar competition at the time. The race itself proved disastrous: mechanical failure after just six laps made him the first pole-sitter since Cliff Woodbury to finish dead-last in the field. He continued as a full-time Indy Car driver through 1990 and attempted to qualify for the 1994 Indianapolis 500 as his final appearance in an Indy car.
From 1985 to 1995, Carter competed in fourteen NASCAR Winston Cup Series races. His debut came at the 1985 Southern 500 at Darlington Raceway, the race famous for Bill Elliott securing the Winston Million. In the 1986 Daytona 500, he was involved in a first-turn accident with Kyle Petty. His best NASCAR Cup finish was seventeenth, achieved at Michigan International Speedway with the Roger Hamby team. He also ran two Craftsman Truck Series races in 1995.
After retiring from driving, Carter transitioned to the role of spotter, working with drivers including Sam Hornish Jr., Dan Wheldon, and others in Indy car racing. In 2019 he was the spotter for rookie Santino Ferrucci, who finished seventh at the Indianapolis 500 and was named Rookie of the Year — mirroring Carter's own debut result in 1974. Carter has continued in the role with Dale Coyne Racing.
Carter was inducted into the National Midget Auto Racing Hall of Fame in 1990 and the National Sprint Car Hall of Fame in 1991, recognizing his championships across both disciplines and his status as the first driver to achieve the USAC midget and sprint car double.