He eventually emerged after nearly two and a half hours with a 5-7, 6-2, 7-6 (4) win - the first by an American in singles at the event since 2007 - having several times come back from what looked like hopeless positions.
While he can technically still reach the semi-finals, his hopes are remote, especially with his final group match being against title favourite Roger Federer. "I think I first qualified for this tournament in Shanghai in 2002 when I was 21, so I'm very excited for Alex - he has a very bright future ahead of him".
Jack Sock kept his hopes alive in the ATP finals with a courageous display, emerging from the brink of defeat to beat Marin Cilic 5-7 6-2 7-6 (4) in a dramatic if erratic battle of the big hitters at London's O2 Arena on Tuesday.
Croatian Marin Cilic celebrates taking the opening set against American player Jack Sock, during day three of the ATP World Tour Finals being played at the O2 Arena in London, Tuesday Nov. 14, 2017.
Federer plays Cilic on Thursday afternoon, clearly created to ramp up day-time ticket sales in a tournament shredded by the absence of the injured Andy Murray, Novak Djokovic, Stan Warwinka, Milos Raonic and Kei Nishikori, as well as the less-than-surprising departure of Rafael Nadal after limping to heroic defeat on one good knee against David Goffin on Monday - and Sock plays Zverev in the evening TV slot.
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Statistically, the last qualifier for these finals was evenly matched with Cilic during the match, but after a run of seven wins in nine matches, his self-belief was high.
But Zverev is setting tongues wagging after an impressive year in which he has won five tournaments, and Federer was forced to repel three break points against the German as early as the opening game. I'm here to win matches. The fire alarm went off at 4:00 am and we had to exit the building. You make me feel at home.
"It was a tough one for sure", he said in his post-match interview on court.
"I'm just going to try to be a little bit more stubborn in my preparations maybe for the next match, and hopefully next year".
Cilic broke for a 2-0 lead in the deciding set, but Sock displayed the fighting spirit that carried him to an unlikely Masters victory in Paris last month, breaking back in the fifth game and force a tiebreak.