Federer defeated the giant South Africa n 6-4, 6-3 in 76 minutes but once he had taken the first set it was already enough to mathematically edge out Austrian Dominic Thiem and Nishikori, and progress through the group named after Lleyton Hewitt.
"I think Thiem winning maybe helped me come into this match a little more relaxed", Federer admitted after the match. "I did a really good job constantly applying the pressure and not letting up", Anderson said.
Having been pummeled 6-0, 6-1 by Anderson on Tuesday, Nishikori made a disappointing start by allowing Thiem to break at the first attempt.
But when asked to reflect on his season, the 28-year-old was positive, assessing his effort as "really good". Both players were close, and the only difference was that Federer needed only one break to win. "I'm not used to losing and then coming back to play, it was a good test". But Federer, who has never looked completely on top of his game this week, suddenly found five excellent points to take the set.
"I think I had an aggressive-playing mindset", Federer said.
Federer, who has only failed to reach the semi-finals in the event once in 15 appearances, will still need to beat group leader Kevin Anderson in straight sets on Thursday to be absolutely sure of making it to the weekend. Record six-time champion Federer turned on the style to avenge this year's gut-wrenching Wimbledon quarter-final defeat by Anderson in which he squandered a match point.
"I am happy it all worked out in the end".
"There were too many unforced errors for me", said Nishikori.
Asked for his thoughts after his round-robin victory over American John Isner at the ATP Finals yesterday, Djokovic said Federer had earned the right for special treatment. Federer said: "I'm very happy, I didn't play well against Kei and had my back against the wall". The following game was also very long and Thiem converted the fifth break point after a double fault from Nishikori, closing the set with a forehand victor in the following game after 41 minutes.
The Japanese world No 9 looked poised to end the season on a high after taking the scalp of six-time victor Federer in their opening round-robin match at London's 02 Arena. "Sometimes I get asked, 'Do you want to play day or night?'" the 20-time grand slam champion told a news conference.
A confident Anderson pushed hard early on and had a glimmer of a chance in the sixth game but Federer held with a sublime backhand victor that had the crowd roaring their approval. "I stayed injury free also, for most of the year, so I am actually very happy with this season so far", he added during a recent interview in London. "But the plus side is I'm through to the semis".