Novak Djokovic secured his place in the semi-finals and cleared the way for Andy Murray to join him at the ATP World Tour Finals.
The world number one beat Tomas Berdych 6-2 7-6 (8-6), meaning Murray would qualify if he took a set off Jo-Wilfried Tsonga on Friday evening.
Third seed Murray duly saw off Tsonga 6-2 7-6 (7-3) to reach the last four.
Djokovic goes through as Group A winner, after Roger Federer qualified from Group B on Thursday.
"I didn't want to think about scenarios or calculations, I'll leave that to other people," said Djokovic.
"I just try to do my job and win on the court. I played a really good match but I thought he served better towards the end of the second set. I was fortunate to come back and win in straight sets."
However, the round-robin system meant he still faced the prospect of an early exit with a poor result against Berdych and he needed to be sharp from the off.
Djokovic was exactly that, firing returns at Berdych's toes and making 74% of his first serves as he raced through the opening set in 34 minutes.
When he broke again in game three of the second there seemed little prospect of the muted afternoon crowd coming to life, but the top seed then handed back the initiative with a poor service game of his own.
It came down to a tie-break and the qualification scenario looked increasingly complicated as Berdych moved 5-1 and then 6-3 up, but Djokovic found two good serves before the Czech netted a backhand.
Djokovic closed it out with a service winner after one hour and 37 minutes to maintain his 100% record and remain on track for a second season-ending title.
"The fact is that it being the last tournament of the year here in London for most of the players, it is a challenge finding that last drop of energy, physical, mental, to find their best game and go as far as they can," Djokovic added.
"So that's in my case, same thing. I played a lot of matches this year but for the first time I won all three in my group. This is very encouraging for me, so I will try to focus on the semi-final now."
And asked about his father, who has been struggling with illness in Serbia, Djokovic said his condition was "better" and added: "Good news every day. (It) makes me happier, makes me play more relaxed on the court.
"I try to switch off on the tennis court. I try to think only about the match and it's been working well so far."