Team Italy needed to win just one match in the tie against France at Ken Rosewall Arena to progress to the quarterfinals and Cobolli did just that on New Year's eve.
Humbert looked set to clinch an easy victory over Cobolli after  putting together a clinical performance to claim the first set within 31 minutes.
But Cobolli dug deep, breaking back after Humbert served for the match before staving off a match point in a tense second set tiebreaker.Â
The world No.14 cracked under the pressure in the decider as he racked up 22 unforced errors to nine, Cobolli pulling off his comeback win in two hours and four minutes.
Italy takes Group D after beating Switzerland 2-0 in their opening match.
"Everything is really fantastic now. It's the last day of the year," Cobolli said.
"It was a great battle to start the season.
"I'm really happy about the match. I played a really good match.
"It was tough to come back against Hugo."
🤯🤯🤯 — United Cup (@UnitedCupTennis) @cobollifla #UnitedCup pic.twitter.com/Xkc8TOqOzmDecember 31, 2024
France needed to win all three games against Italy to keep their campaign alive after they lost 2-1 to Switzerland.
They could progress further in the tournament if they finish the best runners-up out of the three groups in Sydney, meaning they must win the women's and mixed doubles matches.
But France's Chloe Paquet faces a tough challenge, taking on world No.4 Jasmine Paolini in the women's singles.
Kazakhstan, Germany and China have already secured their spots in the quarterfinals, with China having finished the best runners-up team in Perth.
In Perth, the USA play Croatia at RAC Arena with Taylor Fritz first up against Borna Coric before Coco Gauff takes on Donna Vekic.
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