The Swiss No.2 seed squandered a break early in the second set as Zverev upped the ante to force a decider.
They had split their four previous meetings prior to this week but it was Federer who dug deep into his reserves to pull away with two breaks for a 5-1 lead in the third set. He secured passage to the knockouts with a third break courtesy of a Zverev double fault, which was the young German’s 45th unforced error of the match.
“It was a tough group so I’m happy I got through in two matches,” said Federer after the win, adding that he was pleased he can play freely in his next round-robin match against Marin Cilic.
With 16 years separating the two players, you wouldn’t expect them to have already started a budding rivalry.
Yet tennis often knows no age and the Federer-Zverev match-up is already proving to be a blockbuster affair.
After Jack Sock defeated Cilic in a third-set tiebreak earlier in the day, all Federer needed was a win to guarantee a spot in the final four.
Zverev, the youngest top-three players since Novak Djokovic in 2007, will now have to fight off Sock on Thursday for a place in the semi-finals.
“I like what I’m seeing with Sascha. I see somebody who is working towards the future,” Federer said of Zverev. “I think, yes, of course it’s really important right now to have success. He had that with two massive wins in Rome and Montreal. I mean, that’s going to protect his season anyways. The rest sort of is all a bonus.
“What I like to see is I feel like they’re working towards how he could be playing when he’s 23, 24 years old in terms of fitness, planning, organisation, all these things. I think that’s nice to see.
“What I like about Zverev is he’s got the full package. He’s already three in the world. I think he’s going to leave the World Tour Finals, regardless if he qualifies for the semis or not, with a lot of information.
“I think the last six months of the season gave him everything he needs to work forward to. Then, of course, he’s only going to get stronger from here. That should be very encouraging for him and his team.”
On his part, Zverev is confident about his upcoming decisive match with Sock.
“I think I still have great chances of qualifying, playing Jack Sock next. I think if I continue having this level, I don’t know, maybe you’ll see me on the weekend still,” he said.
Japan, USA, Bulgaria, Poland... No matter the nation, Roger Federer is certain to have a legion of fans hailing from it.
He is the universal brand everyone wants a piece of and his tennis fans are as loyal as they come.
We spoke to some of the Swiss legends' aficionados outside the O2 Arena in London, where Federer is gunning for a seventh ATP Finals title.
Check out the video above to meet some of his biggest supporters.
Jack Sock kept his dreams of a fairytale finish to his season alive on Tuesday, beating Wimbledon runner-up Marin Cilic 5-7, 6-2, 7-6 (4) at the ATP Finals.
Cilic, who won the 2014 US Open, broke the American twice to win the first set but found himself adrift in the second as Sock levelled the round-robin match with two breaks of his own.
In a see-saw deciding set, the Croatian fifth seed started quickly and raced to a 3-0 lead before Sock, the eighth seed, steadied himself, cancelling out the break.
The match then settled back on serve and went to a tiebreak. Although Cilic edged ahead 4-2, Sock held his nerve, winning five points in a row to seal the victory.
— Tennis TV (@TennisTV) November 14, 2017
“That was a tough one for sure,” said the American. “It’s been an interesting morning so far. The fire alarm went off at 4:00 am 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.”
He later elaborated in his press conference saying: “At first I didn’t know if it was a test or whatever. Then I realised it was 4 a.m., so I hoped it wasn’t just a test from the hotel. I went outside, saw Rafa (Nadal), saw Dominic (Thiem). Everyone was all bundled up, freezing cold, just wanting to get back inside. Yeah, it was pretty miserable, to be honest.”
Sock, the American number one, came from nowhere to reach the end-of-season event, reaching London by winning the Paris Masters — and breaking a run of European success at Masters events stretching back to 2010.
He is the first American since Mardy Fish in 2011 to qualify for the ATP Finals in singles and on Tuesday, he became the first American to win a singles match at the O2 Arena.
“I’ve been talking to Mardy since I’ve been here. He told me to enjoy it. I know he was the last guy here. I didn’t even know if he’d won a match or not,” said Sock. “That’s news to me. Yeah, going out there and enjoying the moment.”
Sock said he wasn’t necessarily surprising himself with his form this season, and that he turns up for tournaments looking to go deep, not just make an appearance.
“I’m 25 years old. I’m not the new kid on the block anymore. It’s kind of my time, the next however many years. Yeah, I’m just trying to do what I can,” he added.
This week, Sock lost his first match in the Boris Becker group to Roger Federer while Alexander Zverev beat Cilic, leaving both fighting for their lives on Tuesday.
The top two players from each of the two groups of four will progress to the semi-finals.
Cilic admitted it was “frustrating” to lose both of his opening two matches in the same manner, having had it in his hands before letting it slip away.
Is the Croatian feeling jaded at this point so late in the season?
“Well, yes and no. It has been this long stretch. These last couple months, I’ve played a lot of matches as well,” said Cilic.
“Still it didn’t bother me much. I was quite motivated in both matches. I felt that I played well. I know that I wasn’t playing the best, especially in those critical moments I was not coming up with some great shots.
“It’s also end of the season. I think both Alex, and Jack today, they were both as well a little bit up and down with their game, producing some great shots, great serves, some great shots off the run. Overall, I would say it’s quite open in both matches. That was just a little bit unfortunate that I wasn’t able to close. I was putting myself in a really nice position.”
Later, the crowd will be treated to the latest episode in the cross-generational rivalry between Federer and Zverev, with the tournament desperately needing a compelling story after the withdrawal of world number one Rafael Nadal.
The Spaniard quit the tournament on Monday after losing his opening match in the Pete Sampras group to David Goffin.
Federer, 36, and Zverev, 20, have faced each other four times and each has won twice. This year, the Swiss world number two beat the German in Halle but Zverev returned the favour at the Rogers Cup in Montreal.
The ATP Finals feature the top eight fit male singles players and doubles teams who have accrued the most points throughout the 2017 season.