Federer started the match with the same kind of ruthless efficiency that helped him beat Rafael Nadal in just one hour Tuesday, chasing Fish all over the court with his forehand and breaking three times in the first set.
But the Swiss star's accuracy and energy levels dropped in the second, when he started spraying his backhand into the net and let Fish back into the match. The American, looking to leave London with a consolation victory after losing his first two round-robin matches in his debut appearance at the event, raced to a 5-2 lead and served out the set when Federer netted a backhand.
But Federer immediately took control of the deciding set, breaking for a 2-0 lead with a forehand passing shot. The fourth-seeded Federer lost just two points on his serve the rest of the way and converted his first match point when Fish shanked a backhand wide.
"He really started to zone in on many shots" in the second set, Federer said. "I thought he was able to keep that up in the third set. So I was happy to get the crucial break early in the third and maybe cruise a bit more."
Federer already had clinched a spot in the semifinals, while Fish already had been eliminated going into the match.
"Bottom line is I'm going to go away 0-3, which is hard," Fish said. "But I had a great experience just being a part of this. It gives you a lot of ammunition to want to come back next year."
In the late Group B match, Nadal was set to play Jo-Wilfried Tsonga of France, with the winner joining Federer in the last four.
Federer improved his unbeaten streak to 15 straight matches after winning titles in Basel and Paris. The 16-time Grand Slam winner is the defending champion in London and is looking for a record sixth title at the season-ending event for the world's top eight players, and his 70th overall.
Thursday's win was his 37th victory overall at the ATP finals -- previously known as the Masters Cup -- surpassing Boris Becker and putting him two short of Ivan Lendl's all-time record.
Even at 30, though, Federer doesn't feel pressed for time to chase more records.
"I guess I do play for a little bit of the legacy and the history, the record books, all that stuff," Federer said. "But it's really the press that reminds me of most things. I just try to go along with it because I have no intentions to quit. So I can concentrate on just playing tennis at the moment."