Donohue was born in Haddon Township, New Jersey, and grew up in Summit. He graduated from Brown University in 1959 with a degree in mechanical engineering, having begun racing a 1957 Corvette during his final year. He won his first event — a hillclimb in New Hampshire — on debut. Winning the SCCA national championship in an Elva Courier in 1961 brought him to wider attention.
His friendship with the respected sports car driver Walt Hansgen opened doors: Hansgen arranged a co-drive at the 1964 Bridgehampton 500-mile SCCA race, which Donohue won. Hansgen brought him along to Le Mans in 1966, though Donohue's race ended with a differential failure after twelve laps. When Hansgen died during testing for that Le Mans, Roger Penske spoke to Donohue at the funeral about joining his fledgling operation.
Donohue and Penske rapidly became the most formidable driver-team combination in American racing. Donohue dominated the 1967 United States Road Racing Championship, winning six of seven starts in a Lola T70. In Trans-Am, beginning in 1967, his engineering instincts and obsessive preparation gave Penske's Camaros a consistent edge. In 1968 he won ten of thirteen Trans-Am races — a series record that stood until 1997 — and the partnership developed the famous practice of acid-dipping car bodies to reduce weight, strategically placing ballast for optimal balance. Donohue won the Trans-Am Manufacturers' Championship for AMC Javelin in 1971, taking seven of ten races in the over-2.5-litre class.
At Indianapolis, Donohue finished seventh on debut in 1969, then second in 1970, before winning in 1972 with a McLaren-Offy at a record average speed of over 162 mph (261 km/h) — a mark that stood for twelve years and Penske's first Indy 500 victory.
The centrepiece of Donohue's engineering legacy was the Porsche 917/30, developed with Penske and Porsche for the 1973 Can-Am season. The car's 5.4-litre turbocharged flat-12 engine produced between 1,100 and 1,500 bhp, adjustable via a boost knob in the cockpit. Donohue drove it to win the 1973 Can-Am championship, the series losing to the machine almost all competitive interest — hence its "Can-Am Killer" nickname. On 9 August 1975, he drove the 917/30 to a closed-course world speed record at Talladega Superspeedway, averaging 221.120 mph (355.858 km/h), a record that stood eleven years.
Donohue also won the inaugural IROC championship in 1973–74, beating contemporaries including Denny Hulme, Richard Petty, A.J. Foyt, Emerson Fittipaldi, and Peter Revson in identical Porsche RSRs.
Donohue's Formula One career was brief. He finished third at the 1971 Canadian Grand Prix in a McLaren entered by a private team — a podium on his World Championship debut. When Penske formed a Formula One team for 1974–75, Donohue returned. He managed fifth-place finishes at the 1975 Swedish and British Grands Prix in the Penske PC1, but the car proved troublesome.
At the 1975 Austrian Grand Prix, during a practice session at the Österreichring, a tyre failure sent Donohue into the catch fencing at Turn 1. He initially appeared uninjured, but developed a severe headache and was taken to hospital in Graz the following day. He lapsed into a coma from a cerebral haemorrhage and died on 19 August 1975. A track marshal had been killed by debris from the crash. Litigation arising from the accident was settled in 1986, with Goodyear paying Donohue's estate and family $9.6 million.
Donohue's book The Unfair Advantage, co-written with Paul Van Valkenburgh and published shortly before his death, remains a celebrated account of the engineering approach he brought to racing — a meticulous, step-by-step record of developing cars to the limit of what was possible. He was inducted into the International Motorsports Hall of Fame and the Motorsports Hall of Fame of America in 1990. His son David Donohue became a successful road racer. The Penske Racing complex in Mooresville, North Carolina is decorated with murals commemorating Donohue and the cars he drove.