Berrettini, a former world number six, has struggled with fitness issues and missed eight of the 18 Grand Slams since his runner-up finish to Novak Djokovic at Wimbledon five years ago.
On Saturday, the Italian prevailed in a gruelling five-hour battle with Argentina's Comesana, winning 7-6(3), 5-7, 6-7(4), 6-4, 7-6(13).
"I know what it takes to go deep in a slam, but at the same time, it's also true that I haven't been deep in a slam for a long time," Berrettini told reporters after his win.
"Coming into the tournament, I didn't have the confidence, like I had a couple of years ago, but at the same time, I feel like I have built this confidence up.
"I'm in the fourth round, second week of Paris, means that I can go deep. I'm playing well. Today was, I think, a high-level match. My weapons are working, physically I'm there, and fingers crossed."
After the match, Berrettini appeared to be holding back tears as he waved to the crowd at Court Simonne Mathieu.
"I doubted about myself a little bit too much, I think, in the last months and years," the 30-year-old said.
"Even though I had unbelievable support from my family, from my friends, from my team, and everybody kept telling me that I still had it in me. Sometimes I just have to confess that I thought that I couldn't come back, I couldn't feel good on court again.
"That's why I was emotional, because I proved to myself one more time that I can do this, I can do it well, I can fight, I can enjoy my time on court."
Berrettini next faces another Argentinian in Juan Manuel Cerundolo, who beat world number one Jannik Sinner in the second round.