Alcaraz has already cemented his status as a top contender on the biggest stages and is one of the favourites to take on the mantle of his compatriot and 14-times Roland Garros champion Rafa Nadal (36), who is absent this year with a hip issue.
Alcaraz, who missed the Australian Open in January due to a leg injury, was impressive in his first Grand Slam match since his US Open triumph last year and was ruthless as he raced through the opening set.
A fourth break of the contest early in the second set handed Alcaraz, who won the claycourt tournaments in Barcelona and Madrid, the advantage again before Cobolli finally got on the board in his main draw debut at the majors.
Alcaraz comfortably served out to go two sets up but the 159th-ranked Cobolli held his own and threatened to mount a late fightback as he broke to level the third set at 5-5 with some ripping forehands.
However, the top seed stepped up another gear to ensure Cobolli - who promised to get a tattoo of the Roland Garros logo after his qualifying run - would leave the tournament with an abiding image of a chastening defeat.
