Roger Federer put himself in with a chance of progressing to the knockout stages of the ATP Finals after defeating Dominic Thiem in straight sets on Tuesday night.
Federer knew anything other than a victory would see him fail to qualify from the group stage for only the second time in 16 appearances at the Finals.
The 37-year-old six-time winner grabbed a break in the third game against a nervous-looking Thiem, and a second for 5-2 on his way to taking the first set.
Thiem, who also lost his first match to Kevin Anderson, dropped serve at the start of the second set and at again at the end as Federer completed a 6-2 6-3 victory in an hour and six minutes.
Federer will now face Anderson on Thursday, with Thiem taking on Nishikori and qualification for the semi-finals still possible for all four players.
Federer said: "It feels good, I'm very happy I showed a reaction after the last match against Kei.
"No match is easy here and it's not something I'm used to, losing and then coming back and playing again, but it's a great challenge and I'm happy with my attitude and how I played. It was good fun.
"Today I was more positive, more happy on the court and I reminded myself what a privilege it is to play here at the 02."
As if his fearsome display this afternoon was not enough to make Federer wary, Anderson also ended the Swiss star's hopes of a ninth Wimbledon title earlier this year.
"I hope it's not a match like Kevin played this afternoon," added Federer.
"It's never easy to play against him, especially indoors. He deserved that win at Wimbledon but hopefully I'll get my revenge."
Kei Nishikori avoids double-bagel in defeat to Kevin Anderson
Kei Nishikori narrowly avoided only the second 6-0 6-0 defeat in ATP Finals history against Kevin Anderson.
The world number nine beat Roger Federer in the opening round-robin match on Sunday but was a shadow of that player against 6ft 8in Anderson.
Wimbledon runner-up Anderson raced into a 6-0 5-0 lead to leave Nishikori staring at a dreaded 'double-bagel' before the man from Japan finally managed to string a service game together.
It only delayed the inevitable, though, as Anderson duly served out to complete a punishing 6-0 6-1 victory in an hour and three minutes.
Federer therefore remains the only player to dish out a 6-0 6-0 defeat at the Finals, against Gaston Gaudio in the last four in 2005.
Anderson, who also won his opening match at London's 02 against Dominic Thiem in straight sets, said: "It's one of the best matches I've ever played.
"Kei is a world-class player but I just had to take every game at a time. You wait a whole year to play a match like that and it feels fantastic."
Despite the crushing defeat Nishikori will still have a chance of qualifying for the semi-finals if he beats Thiem on Thursday.
"For me, it was one of the worst days in the year," he said. "He was playing well, serving well and returning well, too.
"He played good and it just wasn't my day today. I need to try to forget about today. Something was wrong, I've got to fix it tomorrow and try to be positive for the next one."
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