Federer only has to win five games against Anderson to move to the semi-finals thanks to Dominic Thiem's victory against Kei Nishikori at the start of the day.
The Swiss star has won one of his two round-robin matches and takes the group leader and 20 tonight.
Anderson has already moved to the last four, alongside Novak Djokovic, but will be fighting to win the group.
Federer is concentrating exclusively on victory insurance, which can be a difficult task in itself.
"If I do not pass, I do not pass, and I do not deserve to pass," said Federer.
"It's important for me to play a good last game here in the round-robin, try to beat Kevin, he played great, he had a wonderful season, he played against me at Wimbledon.
"This is my goal, I can not talk about what will come next because it's a tough match in itself.
"My first round match here was not great, so today was better, and I need to keep it against Kevin, of course, if I want to have the chance to stay here in London."
How to watch Roger Federer against Kevin Anderson on TV
Sky Sports and the BBC will broadcast the ATP finals this week.
However, only Sky Sports Arena (Sky Channel 409) and showing this fight by 8pm.
How to watch Roger Federer vs Kevin Anderson online
Sky subscribers can live streaming via SkyGo and the SkyGo app.
The game can be tracked live on your desktop or laptop via the Sky Go app, which if you are an existing customer is also available on iOS and Android smartphones and tablets.
Sky Go is also available on many platforms, including Amazon Fire devices, iPads, Mac computers and laptops, Playing station 3, PS4 and Xbox One.
The Sky Sports app, available for download on iOS and Android devices, will also provide coverage and text updates in real time.
If you are not currently a Sky Sports customer but you can not lose the action, you can add channels to your mailbox via an NOW TV subscription.
Daily passes, which allow you to add Sky Sports channels for 24 hours, start at £ 7.99 a day, with a weekly subscription starting at £ 12.99 and without a block in a a contract.
NOW TV does not even require a typical TV to use, as it is also available on a TV Box NOW, Chromecast, PS4, PS3, Xbox One, Xbox 360, Roku, LG Smart TV, PC or Mac, and on selected mobile devices and tablet devices.