This car's four-wheel-drive powertrain was developed on the previous Delta S4 Group B rally car, which was a Delta in name only, built for the Group B World Rally Championship class and sharing virtually nothing with the Delta production cars. Powered by a turbocharged 2.0-liter "Lampredi" twin-cam, four-cylinder engine, this version made a respectable 163 horsepower and 192 lb-ft of torque. When Group B was canceled, Lancia decided the production Delta HF 4WD would be homologated for Group A and the 1987 WRC season.
After winning its maiden WRC season outright, Lancia developed the Delta HF 4WD into the fabled Delta HF Integrale for 1988, with permanent all-wheel drive and engine modifications to achieve 182 horsepower and 224 lb-ft in roadgoing trim. The race version won the 1988 WRC title, and in 1989 was replaced by the Delta HF Integrale 16v. True to its name, a 16-valve head and other modifications increased power again and won Lancia its third WRC title in a row, with a fourth and fifth to come in 1991 and '92.