Currently ranked third, he won Norma Djokovic a week ago in the Masters 1000 Paris-Versu Semifinals.
In this case, Federer was somewhat slower and never found his rhythm and had never multiplied the error in the hard coat of the London O2 court.
At the start of the second set, even the 'break' could not find a way to win.
Federer has not lost a Japanese player for more than four and a half years at Miami in 2014.
Despite this defeat, Switzerland, which has a record in Masters (16) and tournament (6), has the option to advance to the semi-finals. It must be in one of the first two positions. In the past two groups (2007 and 2013), he lost to his first game and made his mark in the Masters Tournament semi-final.
After Federer defeated Federer, "We are in slower conditions than the last three tournaments I played (Shanghai, Basel, Paris-Bergse). We all need time to adjust.
Anderson can be with Thiem.
South Africa 's Kevin Anderson (sixth in the world), in another match of his "Lleyton Hewitt Group", won the Austrian Dominique team (8th) 6-3, 7-6 (12/10) I scored each set.
Anderson (32) was the first player to win the Masters Tournament in Wimbledon in the year of the 2.03m giant.
"I was a little nervous," South Africa admitted. "But I was able to concentrate quickly, find good rhythms, and look for opportunities when I was serving the service."
Twenty-five-year-old Thiem was in charge of the third Masters but could never pass the group stage in the previous two groupings.
"I did not start well and my first set was not so good, I did not have a chance to ruin his service, and there was a problem in almost every match with my serve," Austria admitted.
"In the second set, there was a very good tennis, with a few balls," added Roland of the Year runners-up.
Servian Novak Djokovic, Serbia's world number one, has set off a fierce battle with American John Isner. Bulgarian Grigor Dimitrov defenders are not eligible to compete in this year's top eight competition.
In London, Rafa Nadal of Spain and Juan Martin Del Potro of Argentina are in second and fourth places respectively and there are two casualties.