Dallenbach was born in East Brunswick, New Jersey. Before entering motorsport, he worked in the construction industry. He began his racing career in modified racing and made a lone stock car appearance at the 1962 Daytona 500. His interests eventually shifted to open-wheel disciplines: he progressed through midget and sprint cars before reaching Indy cars in 1965.
After several years in uncompetitive equipment, Dallenbach's fortunes changed dramatically in 1973 when team owner Pat Patrick signed him as a replacement for Swede Savage, who had been critically injured in that year's Indianapolis 500. Following Savage's death, Dallenbach's place in the Patrick team became permanent. Within four races he scored his first victory at the Tony Bettenhausen 200 at the Milwaukee Mile. He then added two more wins in 1973, including the California 500 at Ontario Motor Speedway. Despite missing four races that season, Dallenbach finished second in the USAC Championship Car standings.
The following years produced some strong performances. At the 1975 Indianapolis 500, Dallenbach led for roughly half the race and engaged in a prolonged battle with A.J. Foyt before a burned piston on lap 162 ended his challenge, just twelve laps before the race was halted by rain and awarded to Bobby Unser.
Dallenbach joined CART as Competition Director in 1980 and was appointed Chief Steward in 1981. Over the following two decades he became one of the most influential figures in American open-wheel racing's administration. He significantly strengthened CART's safety infrastructure, including establishing the first dedicated rapid response trauma team in American auto racing and organizing nondenominational church services for drivers and their families.
One of the defining moments of his tenure came in 2001 when advanced testing at Texas Motor Speedway revealed that drivers were blacking out due to extreme g-forces. Dallenbach had flagged the circuit as unsafe for Indy car racing as early as 1996. Despite significant pressure from commercial stakeholders, he supported the decision to cancel the Firestone Firehawk 600 on race day to protect competitor safety. He initially retired after the 2000 season but returned as Chief Steward when his successor drew criticism from drivers, serving until the end of the 2004 season.
Away from the circuit, Dallenbach became deeply embedded in the community of Basalt, Colorado, where he had purchased a ranch and property using his California 500 winnings. He served as president of the Colorado 500 motorcycle charity ride, an annual event that raised nearly three million dollars for the Basalt community over the years, including more than $800,000 in student scholarships. In 1976 he purchased the first ambulance for the town. In 2023, Dallenbach and his wife returned to New Jersey after selling the Colorado property. He died on April 29, 2024, at the age of 87.
Dallenbach was inducted into numerous halls of fame reflecting both his driving career and his contribution to motorsport administration: the Eastern Motorsport Press Association Hall of Fame (1992), the Colorado Motorsports Hall of Fame (2004), the Sports Hall of Fame of New Jersey (2004), the Motorcycle Hall of Fame (2006), the Motorsports Hall of Fame of America (2020), the Canadian Motorsport Hall of Fame (2021), the Indianapolis Motor Speedway Hall of Fame (2022), and the Pikes Peak Hill Climb Museum Hall of Fame (2022). After his death, the community of Basalt named their newest ambulance in his honor.