In 1968, driving for Alfa Romeo, he finished second in the Targa Florio and fourth in the Le Mans 24 Hours race co-driving with Nanni Galli.

In 1970, Giunti was signed by Ferrari primarily for their sports-car team, and won the 12 Hours of Sebring as well as achieving several other high placings.

His success earned him a Formula One chance along with Clay Regazzoni, who Ferrari was also trialling at the time.

Giunti was killed during his first drive in 1971 whilst racing in the 1000 km Buenos Aires.

He was leading the race when his Ferrari 312PB prototype ploughed into the back of the Matra-Simca MS660 of Jean-Pierre Beltoise, who was pushing the car along the track after it had run out of fuel.