Federer stretched his record to 2-0 at the season-ending tournament for the world's top eight players. Robin Soderling defeated David Ferrer 7-5, 7-5 in the other Group B match, meaning all players still have a chance to advance.
Federer has won this tournament four times, and the second-ranked Swiss can certainly add to that if he keeps playing as he has of late. Against Murray, he lost only eight points on his serve in the match at the O2 Arena.
"I'm surprised, I really am, that I was able to win my service games that comfortably," he said. "That's not to the norm against Andy, who is one of the best return players, if not the best, in the game right now. So I'll take that is all I can say."
Murray dropped to 1-1 and will have to improve to reach the semifinals. He will face Ferrer in his final match Thursday while Soderling takes on Federer.
Besides controlling play with his serve, winning 88 percent of the points when he landed his first serve, Federer forced Murray into long rallies when he was receiving. Pulling forehands to his left and hitting them to his right with ease, Federer waited for his British opponent to make errors or set up his winners.
"He came out and made some mistakes. Maybe it was due to my good play," Federer said. "I played tough and solid from start to finish. That seemed to be enough today."
Murray struggled from the start Tuesday, forced to save a break point in the opening game. And it was his serve that was letting him down most of the way, landing only 44 percent of the first serves. That allowed Federer to take advantage of the much slower second serve.
"I returned poorly, served poorly," Murray said. "Against him, that's not going to win you the match."
Federer earned his first break in the third game of the first set, winning all four points played. He then won his next three service games at love.
In the second set, Murray saved two break points in the opening game, but Federer stayed alive through four deuces to earn a third break point, which he converted with a forehand that hit the top of the tape and zipped past Murray.
After holding at love yet again, Federer broke again to make it 3-0 and soon led 4-0.
"I tried to play quite aggressive. You're not going to hit winners every single time you go on the court," said Murray, who is 8-6 overall against Federer. "Today I made more mistakes than normal."
In the late match, the fourth-ranked Soderling broke his Spanish opponent in the final game of both sets. The Swede also broke the seventh-ranked Ferrer again for a 4-2 lead in the second, but the Spaniard broke back to 5-4.
Soderling lost to Murray in the first match but can still advance with a win over Federer on Thursday, depending on the result in the Murray-Ferrer match. Ferrer has a slim chance of advancing but must beat Murray in straight sets and hope Federer defeats Soderling.
"This was a really important win. Now at least I have the chance to make it to the semis," Soderling said. "[Federer] is playing really good right now. He played two unbelievable matches so far in this tournament. But like always against him, I need to serve and return well and try to be aggressive."
On Monday, top-ranked Rafael Nadal rallied to beat Andy Roddick 3-6, 7-6 (5), 6-4 and third-ranked Novak Djokovic defeated Tomas Berdych 6-3, 6-3. Nadal will take on Djokovic on Wednesday, and Roddick and Berdych play in the early Group A match.
In doubles, Jurgen Melzer of Austria and Philipp Petzschner of Germany beat Lukas Dlouhy of the Czech Republic and Leander Paes of India 7-6 (9), 4-6, 10-8. Mariusz Fyrstenberg and Marcin Matkowski of Poland defeated top-ranked Bob and Mike Bryan of the U.S. 2-6, 7-6 (4), 10-8 in the late Group A match.