The 37-year-old six-time winner knew anything other than victory would see him fail to qualify for the last four for only the second time in 16 appearances at the O2.
But it was a vastly more upbeat Federer who pulverised Thiem 6-2 6-3 than the grouchy character who had trudged off court 48 hours earlier.
However, the 20-time grand slam champion still needs to beat the in-form Kevin Anderson, who knocked him out at Wimbledon and who dropped just one game against Nishikori in Tuesday afternoon's match, if he is to clamber out of the group.
Federer grabbed a break in the third game against a nervous-looking Thiem and a second for 5-2 on his way to taking the first set.
Thiem, who also lost his first match, to Anderson, dropped serve at the start of the second set and at again at the end as Federer wrapped up victory in an hour and six minutes.
He said: "It feels good, I'm very happy I showed a reaction after the last match against Kei.
"No match is easy here and it's not something I'm used to, losing and then coming back and playing again, but it's a great challenge and I'm happy with my attitude and how I played.
"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."
Anderson had previously underlined his credentials as a major contender in London with a brutal destruction of Nishikori.
Japanese world number nine Nishikori was on cloud nine after stunning Federer, but he was brought crashing back down to earth the O2 debutant.
Nishikori was staring down the barrel of the ultimate humiliation, and only the second 6-0 6-0 defeat in the history of the Finals, following a ruthless display by the South African.
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'.
It only delayed the inevitable, though, as Anderson duly served out for a 6-0 6-1 victory in 63 hopelessly one-sided minutes.
"That's amongst the matches best I've played," said Anderson.
"I got off to a really good start and I think I did a really good job constantly applying the pressure and not letting up.
"I was growing in confidence and he sort of probably was going a little the other way, which is tough given the situation."
Anderson is in pole position, but qualification for the semi-finals is still possible for all four players.
Britain's Jamie Murray and Brazilian partner Bruno Soares clinched their place in the semi-finals of the doubles for the third straight year.
Murray and Soares ran out 6-4 6-3 winners against Colombian duo Juan Sebastian Cabal and Robert Farah to ensure their progress with a match to spare.