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.
Tournament debutant Anderson leads the group with two wins and would have been assured of a semi-final spot had Federer been beaten by Thiem or even dropped a set.
The six-time champion will next take on Kevin Anderson, who beat Nishikori 6-0 6-1 earlier on Tuesday.
"I'm happy I'm getting a chance to play him again and have a rematch", Federer said.
Yet 48 hours later, the 37-year-old Federer rebounded in style, to the delight of the crowd packed into The O2 arena.
Violence calms in Yemen's Hodeida amid diplomatic pressure
Britain is seeking support among regional partners for new action at the UN Security Council for peace talks in Yemen . Three port employees reached by telephone said the rebels had also begun to mine entryways to the port overnight.
If Nishikori beats Thiem in straight sets this afternoon then Federer is in severe trouble as he must beat in-form Anderson in the same manner, or else he is out. Federer, who lost their Wimbledon quarter-final clash this year, said on court.
"I am happy I am having a chance to play him again and I hope to get my revenge", he commented after beating Thiem.
Thursday will see members of Group Lleyton Hewitt fight for their lives to advance to the semi-finals here at the O2 in London, with all four players still in with a shout of qualifying.
The 32-year-old won the first 11 games against Nishikori before his relieved opponent finally got on the scoreboard with an angled victor.
Anderson was brimming with confidence, being nearly untouchable on serve and made some powerful returns followed by loads of pulsating groundstroke to steamroll the Japanese No. 1, serving him a nice bagel and taking the opening set 6-0.
'It hits hard': Saskatoon comic book artist pays homage to Stan Lee
Fans argued back that the celebs were celebrating that special moment they got to meet the comic book legend himself. Reacting to the gaff in good humour, Spike, 61, posted the newspaper cover with the caption: "God Bless Stan Lee .
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.
Federer said: "I get asked, would you like to play Monday or Tuesday sometimes". The Swiss superstar has an impressive history at the end of year event.
"I think I did a really good job constantly applying the pressure and not letting up".
Anderson looks nearly certain to reach the semi-finals even if he is beaten by Federer on Thursday. I felt that way today.
More tour dates for Spice Girls, but still no Irish dates
Bunton, however, does say they asked Posh if she wanted to be involved, and agrees with Horner that the "door is open". The remaining members' interview with Jonathan Ross will air tonight in the UK.