ATP Finals: Jack Sock beats Alexander Zverev, Roger Federer beats Marin Cilic
|Venue: The 02 Arena, London Dates: 12-19 November|
|Coverage: Watch live on BBC Two, Red Button, BBC Sport website and mobile app, listen on BBC Radio 5 live sports extra and follow text updates online.|
American Jack Sock came through a pulsating "rollercoaster match" to beat German third seed Alexander Zverev and reach the last four at the ATP Finals.
Eighth seed Sock won 6-4 1-6 6-4 to clinch second place in the Boris Becker Group ahead of Zverev, and set up a semi-final against Grigor Dimitrov.
Roger Federer earlier beat Marin Cilic 6-7 (5-7) 6-4 6-1 to head into the semi-finals with an unbeaten record.
The Swiss, 36, had already topped the group with wins over Zverev and Sock.
Saturday's semi-final line-up will be completed by the winner of the Pete Sampras Group match between Dominic Thiem and David Goffin at 14:00 GMT on Friday.
"Knowing I was qualified on Tuesday evening - it's kind of weird to be already through to the semis, but of course it gives me a great idea how I want to prepare for Saturday," said Federer.
"One more last weekend, one more push before the vacation and then preparation for the next season."
'I kept fighting' - Sock
Sock came into the tournament as the outsider, having admitted he did not even know qualification was possible when he began the surprise run to the Paris Masters title that clinched his place.
It is the 25-year-old American who will line up for the semi-finals on Saturday, however, after he proved too strong for rising star Zverev on a gripping evening at the O2 Arena.
"That was a rollercoaster match," said Sock.
"He played well in the second, I didn't have the hottest start in the third, but I kept in there and kept fighting."
The feisty Sock picked up a code violation as early as the second game for smacking a ball away in anger, which appeared to annoy Zverev.
It was the American's tactical game plan of slicing his backhand, drawing errors from the Zverev forehand, that gave him the edge in the first set.
Zverev, 20, got a grip on his game early in the second, a superb wrong-footing forehand helping him break for 2-0, and Sock's challenge faded inexplicably over the next five games.
The German looked set to take his expected pace in the semis when he fought back from 4-1 down to level in the decider, with Sock picking up a point penalty for furiously firing another ball into the air, but the American clinched the last two games to extend his surprise run.
"I choked," said Zverev.
"It's quite easy. Won the second set 6-1. I was 1-0 with a break. He got a point penalty. I was down 1-4 within 10 minutes where I didn't put many balls in the court.
"When I got back at 4-5, that's one of the worst games I think I played all year."
Russell Fuller, BBC tennis correspondent
Sock's calling card has always been his heavily spun forehand, but he has shown here in London that there is a lot more to his game.
Some exquisite volleying and some clutch serving got him out of tight spots against Zverev - as did the release of firing a couple of balls high into the stands.
Sock was docked a point for his second offence but remained the steadier down the stretch to become the first American to reach the semi-finals of this event since Andy Roddick in 2007.
Not bad for a man who did not think he could qualify for London when he arrived in Paris - only to win the final event of the regular season.
'I was in trouble' - Federer
Federer and Cilic met for the first time since a one-sided Wimbledon final, which saw the Swiss win a 19th Grand Slam title as Cilic struggled with a blister on his foot.
The Croat put up sterner resistance for the better part of two sets at the O2 Arena, before Federer ran away with the contest, winning eight of the last nine games.
Federer could have made shorter work of it had he converted one of three break points in the opening game but Cilic clung on, and a beautiful backhand volley at 5-5 in the tie-break saw the fifth seed edge ahead.
A break point early in the second set offered real opportunity for Cilic but Federer stood firm at the net, and once he finally broke serve to take the second set there was only one winner.
The Swiss six-time champion raced through the final set to reach the semi-finals for the 14th time in 15 appearances at the ATP season finale.
"I think it was a tough match, a lot of chances maybe in the first set," said Federer.
"I think Marin served well and was a bit better in the breaker. I was in trouble a set and a break point down in the second set, so I'm happy I found a way out of it and in the end I played really well."