Current number 3 on the male rank had nothing to do with the player who was close to beat Novak Djokovic in the semi-finals of the Masters 1000 Paris-Bercy just over a week ago.
At this point, Federer was a bit slow and never found his rhythm, and multiplied the flaws in the London O2 hard casing.
Not even a "break" at the start of the second set made him find the way to victory.
Federer did not lose to the Japanese player for more than four and a half years, in the Miami tournament in 2014.
Despite this defeat, the Swiss, who has a record of participation in the champions (16) and the titles of this tournament (6), still has the opportunity to reach the semifinals, for which he must be in one of the first two positions of the group. Twice earlier (2007 and 2013), he managed to reach the semifinals of the "Masters Tournament" after losing in the first game.
"The game conditions are slower here than in the last three tournaments I've played (Shanghai, Basel and Paris-Bercy.) We all need an adaptation time, I too, says Federer after his defeat.
Anderson can with Thiem
In the second game of his "Lleyton Hewitt Group", South African Kevin Anderson (6th in the World) won the Austrian Dominic Thiem (8th) in two sets, 6-3, 7-6 (12/10).
Anderson, 32, competes "Masters Tournament" for the first time in his career, in a year where the 2.03m giant was runner on Wimbledon.
"I was a little nervous," acknowledged the South African. "But I could focus quickly and find a good rhythm, take care of my serving and find opportunities when he served," he added.
Thiem, 25, plays his third champion, but in the previous two he could never come across the group scene.
"I did not start well, my first bet was not so good, I had no chance of breaking his favor and I had trouble in almost every game with my serving," acknowledged the Austrian.
"In the second set, there was a very good tennis, determined by some balls," added Roland Garros this year.
World number 1, Serbian Novak Djokovic, the second group's favorite, comes into the crime on Monday against the American John Isner. The defender of the title, Bulgarian Grigor Dimitrov, is not qualified for this competition, which brings together the best eight years of the year.
In the London meeting there are two accidents, Spanish Rafa Nadal and Argentine Juan Martin Del Potro, second and fourth in the world, who went to attend their physical problems.