He will next take on in-form South African, Kevin Anderson, who humbled Nishikori 6-0 6-1 earlier in the day. He wasn't getting too many free points. "There were some lucky points but I played well today", said Nishikori.
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.
The Swiss maestro found himself with his back to the wall after an error-strewn loss to Kei Nishikori in his opening round-robin match - his first straight sets defeat in 46 group stage matches at the season-ending showpiece.
"I was not feeling good to play such a match in front of such a big crowd and everything".
"I am very happy that I showed a reaction after the last match", said Federer, who will attempt...
"I felt I did a fantastic job throughout really". Today was a bad match.
Anderson's final group match is against Federer on Thursday, while Nishikori faces Thiem.More news: Trump wants 'rules and regulations' for reporters
"The girls also play a little bit", the world No. 3 continues.
Unfortunately for Nishikori he may just find Thiem in a determined mood to put things right after a shoddy set of performances in London, and he may drop a vital set. "I've got to fix it and try to be positive for next one".
That lone flop came 10 years ago when the Finals were held in Shanghai and Federer is still in with a chance of avoiding that ignominious fate thanks to his comfortable 66-minute dismissal of Thiem.
But Nishikori seemed to have nothing left after that effort.
Anderson won the Vienna final at Nishikori's expense in October, before losing to the Japanese star in the Paris Masters four days later. Novak Djokovic asks Roger Federer question at ATP Finals Novak Djokovic defends youngsters after Federer and Anderson humblings However, even if the 20-time Grand Slam victor does record a comfortable victory, progression would then go down to the percentage of games won between those also tied on two wins.
Anderson is back in London just four months after losing his first Wimbledon final against Novak Djokovic, and this was the kind of dominant display that carried him to the title match at the All England Club.
Two tame volley errors by Thiem gave Federer another break for a 5-2 lead as he cruised to the opening set.