Following an early exchange of breaks on a blustery day, Auger-Aliassime pounced on Cobolli's serve in the 10th game to claim the opening set, after which the roof on Court Philippe Chatrier was closed.
Cobolli, one of three Italian men still in the men's draw after Jannik Sinner's premature exit, battled back from 1-3 down in the second set with the playing conditions suddenly improving.
Having levelled the contest at one set apiece, the 10th seed dialled up the intensity in the seventh game of the next set and put himself just one set away from his maiden Grand Slam semi-final appearance.
The 24-year-old thumped his chest when he edged ahead in the fourth set, and he went on to comfortably secure the victory. He will now await the winner of the all-Italian clash between Matteo Berrettini and Matteo Arnaldi.
