Federer into last four
Roger Federer prevailed 7-6(6), 5-7, 6-1 over Alexander Zverev in a high-quality affair that resulted in the Swiss reaching the semi-finals of the ATP Finals for the 14th time in 15 appearances.
With Rafael Nadal withdrawing from the tournament through injury, Zverev - who is the only player to beat Federer in a final this year - had emerged as the biggest threat to the world No.2 in London, and this marquee encounter lived up its billing.
After Federer was forced to fend off three break points in his opening service game, the pair raced through the first set, reeling off quick hold after quick hold until Zverev saved two set points at 5-6, with one courtesy of a net cord that dropped dead on Federer's side.
The young German took a 4-0 lead in the resulting tie-break, but Federer rallied, winning eight of the next 10 points and saving a set point at 5-6 down to claim the first set.
The Wimbledon singles champion looked on course for victory after breaking in the first game of the second set, but Zverev refused to fade, breaking back at 0-2 and then again at 6-5 to force a decider.
Having landed just 43% of his first serves in the second set, Federer regained his poise in the third, varying his strokes to great effect as he quickly accelerated away from his young opponent; from 0-1 down, the Swiss embarked on a six-game winning streak to become the first man into the semi-finals.
"I'm extremely happy...it's been a tough group so to be there in two matches is great,” Federer said.
“But today was difficult. Still early days in the tournament. It was nice to be able to show maybe that quality of mine, that I can dig out these matches, these points time and time again, stay mentally tough. In the third I started to play better. It was a tough match from the beginning till the end."
Second place in the group will now come down to a straight shootout between Jack Sock and Zverev, and the world No.3 was confident of sticking around in London a little longer.
"I think it was a very positive match,” Zverev said. “I think if I continue having this level, I don't know, maybe you'll see me in the weekend still."
Sock fights back
Jack Sock became the first American to win an ATP Finals match in exactly a decade after recovering from a series of deficits to down Marin Cilic 5-7, 6-2, 7-6(4).
Knowing that defeat could well result in elimination, both men made a fast start to the encounter, flying through holds having initially exchanged breaks of serve in the opening two games.
The duo began to probe for opportunities as the opening set reached its climax, with Sock forging a break point at 5-5 courtesy of a perfectly-executed lob over his 6ft 6in opponent.
But it was Cilic who would make the breakthrough, with the Croatian going after the Sock serve at 6-5 before taking the opener with a belting forehand winner.
Sock's frustration was evident, but he quickly went about getting over his disappointment by breaking Cilic at the first opportunity in the second set. Rather than be buoyed by his first set success, Cilic began to falter, unable to cope with Sock's blend of heavy forehands and smart dropshots, and the American raced away to force a decider.
Just as in his encounter with Zverev, Cilic broke for an early lead in the third set, but he was once again pegged back for 3-3. After six relatively comfortable holds, the pair needed a tie-break to separate them.
The first mini-break went the way of the Croatian, and he prepared to serve at 4-3 having won 15 consecutive points behind his own deliveries. But Sock, who had been chasing down lost causes all afternoon, showed remarkable footspeed to get to a Cilic backhand that had trickled over the netcord, and from there on it was he who played the braver tennis.
Having opted for a sliced backhand for much of the match, Sock powered his double-hander up the line to set up match point, which he converted when a Cilic backhand went long.
"I think if I do the right things and I play the right tennis, I can give myself a chance to play on the weekend of any tournament," said Sock.
"I think I've showed that more this year."
Having failed to capitalise on his third set leads against both Zverev and Sock, Cilic would later be eliminated courtesy of Federer's victory, but will now face the Swiss in a repeat of this year's men's singles final at Wimbledon.
On the morning of his victory, Sock found himself waiting outside his hotel at 4am due to a fire alarm going off. Here's what he made of it...
"It was probably one of the most annoying noises I've ever heard in my entire life. At first I didn't know if it was a test or whatever. Then I realised it was 4am, so I hoped it wasn't just a test from the hotel.
"I went outside, saw Rafa, saw Dominic. Everyone was all bundled up, freezing cold, just wanting to get back inside. It was pretty miserable, to be honest. Everyone obviously put on clothes. It was pretty cold outside.
"The process, I probably waited in the room for five, seven minutes, then probably outside for another five or seven. The whole thing was probably 15 minutes of freezing, miserableness."