Trust in raw talent is no guarantee of victory in any sport, and it was tested to snapping point when Roger Federer survived a serious examination of his pedigree to advance to the semi-finals of the ATP World Tour Finals, while Jack Sock also stayed in the race.

Sock, full of American swagger on his first visit to the singles tournament, beat the 2014 US Open champion and this year’s Wimbledon finalist Marin Cilic 5-7, 6-2, 7-6 (4) in two hours and 37 minutes in the afternoon, while Federer, who has won six of these end-of-season titles, beat the rising Alexander Zverev 7-6 (5), 5-7, 6-1 in the evening. It took the Swiss two hours and 11 minutes, although not all of that experience was entirely serene.

Federer plays Cilic on Thursday afternoon, clearly designed 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. Sock plays Zverev in the evening TV slot.

Federer, who had not dropped a set here this week, said courtside after a rousing comeback against Zverev: “It was a good battle. I was trying to put a lot of balls in play. It was tough. I don’t think I qualified for the ATP World Finals at 20. I’m very excited for his future. He’s a great guy. I’m relieved that in the last match I can play freely against Cilic. Maybe now I can work on my game a little.”

Reflecting on his performance, he told Sky: “I’m using the slice behind the baseline normally but I got stuck, a little too passive a few times. I struggled on the offence a few times today. [But] I’m qualified again for the semis. I couldn’t be happier.”

After 24 games, Zverev, already No3 in the world – the ranking that the injured Murray held in absentia until tumbling to No16 in the world – held three set points on Federer’s serve, and the arena was on edge all around the 20,000 seats as the Swiss strained to keep the contest down to two sets and an early night.

The tension remained ramped to the limit as a wayward Federer backhand allowed the Russian-German to level at a set each. They had been playing for precisely two hours, a symmetry that would soon be ripped asunder. The finish was nowhere near as fraught as the beginning.

Federer had lost only four times in 53 matches this year: but only the Russian Evgeny Donskoy in the second round in Dubai in February, and Tommy Haas, at the first time of asking in Stuttgart in June, had beaten him from a set down.

When Zverev blew a 40-0 lead with a lazy forehand to drop serve for 1-4 in the third, the game looked pretty much up. A double fault to hand Federer victory was more than symbolic. Zverev was tired, spent and well beaten.

In an must-win match, Zverev has to defeat Sock on Thursday. It won’t be easy.

“That was a tough one, for sure,” Sock, here for the first time in singles, said after beating, the Croatian’s seventh defeat in eight matches here over the years. “It’s been an interesting morning so far,” the American said. “The fire alarm went off in our hotel at 4am.

“I love playing in London. You make me feel at home. My coach nicknamed me Showtime when I was young because I always love to play in front of people. There’s always a lot going on. I don’t even know what I’m doing some times.”