The Swiss star suffered a shock opening-round defeat against Nishikori before seeing off Thiem in straight sets in round two.
He kept alive his hopes of advancing from his group with 6-2 6-3 win over the Austrian.
Tournament debutant Anderson leads the group with two wins after thrashing Japan's Kei Nishikori 6-0 6-1 earlier and would have been assured of a semi-final spot had Federer been beaten by Thiem or even dropped a set.
"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 hope it is not a match like Kevin Anderson played this afternoon!"
There is still work to do for the second seed, however, especially as giant South African Kevin Anderson, who he plays at the conclusion of the group on Thursday, is in red-hot form.
"I get asked, 'Would you like to play Monday or Tuesday?' some times".
"Today I was more positive, more happy on the court and I reminded myself what a privilege it is to play here at the O2".More news: Steve Waugh says he played better Indian teams than the current one
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He certainly looked back in the groove, making only 11 unforced errors, compared to the 34 against Nishikori, and surrendering just six points on serve.
Thiem, who also was broken in the seventh game of the first set and the first and last games of the second set, won a respectable 50 percent of his second-serve points but just 56 percent of his first-serve points.
It only delayed the inevitable, though, as Anderson duly served out for a 6-0 6-1 victory in 63 hopelessly one-sided minutes.
To start the second set, Federer played a couple of penetrating rallies, with the single hander working in full flow, and with a little help from Thiem's forehand, got the break immediately.
"And I don't think there's a tournament director in the world who is not going to take those factors into account when setting the schedule".
"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.
"I don't really feel that I am in the mood during a World Tour Finals to discuss that topic, to be honest".