Earlier, Matteo Bertini fought the former Wimbledon Championship again to hit Alexander Zverev, the German seed.
The defeat of ZVEREV in second place means that Jannik Sinner is guaranteed to stay first in the world when it returns from the prohibition of doping for three months in the Italian Open in May.
Zverev twice introduced Berrettini in an opening group of leaders, but the Italian seized his first opportunity for the match in the second group to force a decision.
Berrettini served the match at 5-3 in the third, but ZVEREV responded with a good return game to settle the group.
However, Berrettini erupted again and held his nerves to present a third group of 68 minutes.
After the biggest victory in his career through the arrangement, Berrettini is waiting for either the Lorenzo mustti citizen or the Cheri Lehecka in the third round.
Also on Tuesday, the hero Stefanus Tsissibas returned from a group to win Jordan, Jordan Tomson, 4-6 6-4 6-2.