Anderson, who opened with a straight sets win against Dominic Thiem, tops the Lleyton Hewitt group and will reach the semi-finals if Thiem beats Federer later.
"I just went into the match and wanted to show my real self again, basically, because two days ago (against Federer) was really bad", said the French Open runner-up.
"I am happy I am having a chance to play him again and I hope to get my revenge", he commented after beating Thiem.
Thiem has only won two of his eight matches at this tournament while a win for Federer against Kevin Anderson in the last round robin match on Thursday could send Federer through and in search of a seventh ATP Finals title, though the result of the Nishikori vs. Thiem match will play a part.
"I could win and still not make it, so from that standpoint it's not in my power", Federer said of his clash with Anderson who he lost to in an epic Wimbledon quarter-final this year.
A big key for the Swiss was his play on serve, as he did not face a single break point during the one-hour, seven-minute match and won 86 percent of his first-serve points and 81 percent of his second-serve points.
"I don't really feel that I am in the mood during a World Tour Finals to discuss that topic, to be honest".
It was a landmark moment for Anderson, who has set a new career-high of 47 victories in a calender year.
The Japanese world number nine 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.
"I think I made it really easy today".
If Federer looked bad-tempered and off his game in losing to Kai Nishikori on Sunday, Tuesday saw the return of the calm and controlled Federer, who was totally in control of his game.
"I was growing in confidence and he sort of probably was going a little the other way".
The 2.03-meter Anderson served 10 aces, including three in a row in the third game of the opening set. "There were some lucky points but I played well today", said Nishikori.
It's also no exaggeration to say that if Anderson performs as he did against Nishikori on Tuesday, then he can beat Federer in this form.
"Something was wrong. I've got to fix it tomorrow and try to be positive for the next one", the 28-year-old world number nine told reporters.
Anderson looks nearly certain to reach the semi-finals even if he is beaten by Federer on Thursday.