In his news conference shortly afterwards, the 24-year-old said he had found somewhere to stay for the evening.
“My grandfather help us to found a solution for tonight. But we found solution for all the week, I hope,” he said.
“An Italian family give us all the house here in Wimbledon, so it’s really cool.
“I will say thanks to them when I see them.”
The match on Court One was twice interrupted by medical incidents in the crowd as temperatures reached 31C on Monday.
Cobolli and De Minaur sat together in the shade and chatted to each other and the crowd during one break.
De Minaur had a 5-2 lead in the second set, only for Cobolli to wrestle back the advantage and ultimately take control.
The Australian has never gone beyond the quarter-finals of a major in seven appearances.
“It breaks me inside. That’s the reality of it,” De Minaur said.
“To not step up to the plate, it’s truly gut wrenching.
“The goals, the beliefs, the dreams you have, they start fading away or they feel a little bit further away than when they once were.”
Later, sixth seed Taylor Fritz continued his bid for a first Grand Slam title with a 7-6 (7-1) 6-4 6-4 win over 10th seed Alexander Bublik.
American Fritz could play French Open champion Alexander Zverev next, with Fritz having won their past seven meetings.
German second seed Zverev will have to return on Tuesday to complete his match against Czech Jiri Lehecka on Centre Court.
Zverev led Lehecka 6-4 7-5 3-3 when play had to stop because of the Wimbledon curfew of 23:00 BST.
