But 48 hours later, the 37-year-old Federer renewed his style thanks to the delight of people packed in the O2 arena.
Thais kept a break in the opening match, but he sent a forehand long to Federer's early break and was stopped again at 5-2 because Federer was on the cruise to the opening kit.
Federer turned the screws to stop again in the second set, and never saw any danger.
"It feels good, I'm very glad I found the reaction after the last match against Kei," Federer said.
"There are no opponents here, and this is not something I'm used to losing and then returning and playing again, but it's a big challenge, and I'm happy about my attitude and how I play."
Federer will fight South Africa Anderson in their final group play on Thursday.
The tournament debutant Anderson will lead a group with two wins and be sure of the semi finals if Federer has defeated Thiem or even dropped the set.
The 32-year-old won in the first 11 games against Nishikori before his liberated opponent eventually won the scoreboard with an angled winner.
"Among the best (in games) I have played," said Anderson, who lost only eight points.
"I felt that I really did a fantastic job."
Federer will probably be revenging on his Wimbledon losses this year for Anderson in order to reach the semifinals, although all four team members could still math.
"I hope it's not the game Kevin played this week," Federer said.
"It's never easy to play against him, especially on the premises. He deserves this victory at Wimbledon, but, hopefully, I'll get my revenge."