Federer won 7-6 (8-6), 5-7, 6-1 to cement his place in the last four at the O2 Arena in London.

The Swiss legend is now through to the semi-finals for the 14th time and there would appear to be little in the way of stopping him.

"It was a good battle and I always enjoy myself at this beautiful arena," he said.

"I have so much fun playing in London and I have been so successful here. 

"Thank you for making it such a special night."

At 36 he was playing a man 16 years his junior. 

Asked if he remembers what it was like playing the top players when he was Zverev's age, he said: "It was so long ago I hardly remember.

"I don't think I qualified until I was 21 in Shanghai. 

"It was a dream for me to be part of it, where the best players take part and you can slog it out against them, knowing you're only going to get better.

"I'm excited for Alex's future. 

"He's a wonderful guy and a great, great player.

"I'm happy and relieved that I can play freely against [Marin] Cilic, instead of it being a nail-biter.

"It's been a tough group so to be through in two matches is great."

Federer finishes top of the Boris Becker group after two consecutive wins.

Zverev and American Jack Sock will now battle it out for a place in the last four but Cilic has been knocked out of contention.

Earlier, American eighth seed Sock boosted his chances of reaching the last four with victory over the Croatian fifth seed.

Sock won a see-saw encounter 5-7, 6-2, 7-6 in the second round of group matches in the flagship London event.

It means his chances of reaching the last four, which looked far-fetched when he lost heavily to Swiss second seed Federer in his opener on Sunday (November 12), are much improved.

"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, who won three ATP World Tour titles this season, including the Rolex Paris Masters earlier this month.

"I think I've showed that more this year."

Sock held his nerve when it mattered most to win a thrilling last set tie-break 7-4.

The defeat was another heartbreaking loss at The O2 Arena for Cilic. 

"That tie-break, it was quite a few close points," the Croatian said.

"Him getting that unbelievable [net] cord, one backhand down the line that he hit on 5-4. 

"He didn't hit many down-the-line winners during the match. 

"That was a big shot to hit at that stage.

"I think Jack is playing really good. 

"He had a really nice season, especially the beginning, now the end... 

"Overall I think he's playing good tennis, quite aggressive. 

"When he's playing well, he's definitely very dangerous."

The top two players from each group qualify for the semi-finals and after top seed Rafa Nadal pulled out through injury Federer is now a massive odds-on favourite to win the tournament.

"That was a tough one for sure," added Sock who will look to go to 2-1 when he faces Zverev on Thursday (November 16).

"It's been an interesting morning so far, the fire alarm went off at 4am and we had to exit the building. 

"But I love playing here in London, it's an amazing atmosphere, you make me feel like home.

"I'm just excited to win and keep myself alive."

Cilic is making his third appearance at the season finale, and was looking to bolster his chances of making the semi-finals for the first time. 

The Croatian fell to Zverev on Sunday after leading by a break in the third set.

"Definitely disappointing in both matches in that third set, being in a good position, putting myself in a good position," he said.

"But unfortunately I didn't close it.

"What makes the difference I think with these top guys, if you don't take the chances, it's one point here and there.

"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. 

"Hopefully I'm going to perform better."