To maintain his hopes of advancing to the semi-finals of the prestigious tournament, the six-time season finale champion ousted Thiem 6-2, 6-3 in his second round-robin match that lasted 67 minutes.
The Swiss star suffered a shock opening-round defeat against Nishikori before seeing off Thiem in straight sets in round two.
Bidding for a record seventh ATP Finals crown and a first in the tournament since 2011 - which would be the 100th singles title of his glittering career - world number three Federer must beat South Africa's Kevin Anderson in his last group match to make the semi-finals.
The 32-year-old debutant at the ATP's blue riband event won the first 11 games of the round-robin clash, before a relieved Nishikori finally got on the scoreboard with an angled victor. "He deserved that win at Wimbledon but hopefully I'll get my revenge", Federer said of his Anderson rematch.
On the other hand, Nishikori landed only 45% of the first serve in and that was a recipe for a disaster, losing 57% of the points in his games and getting broken five times from 12 chances he gave to Anderson.
Yet at 6-0 5-0, and with less than an hour on the clock, the 28-year-old finally managed to string four serves together to get on the scoreboard and avoid the dreaded "double bagel".
"I get asked, 'Would you like to play Monday or Tuesday?'" Federer explained.
"I'll try to forget about today", Nishikori said.
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After suggesting that the whole debate has been taken out of context, Federer told reporters there is no obvious pattern in the way the timing of his matches is arranged.
"I don't even know why I didn't play well".
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.
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.
"I don't really feel that I am in the mood during a World Tour Finals to discuss that topic, to be honest".
Anderson won the first 11 games, and needed only 64 minutes to demolish the woeful Nishikori in a remarkably one-sided group stage clash at London's O2 Arena.
Federer will likely have to avenge his Wimbledon loss this year to Anderson to reach the semi-finals, although all four players in the group could still mathematically progress.