The exhibition event, which is not part of the ATP Tour, features six of the top 10 players and offers a winner-take-all prize of $250,000.
Murray improved to 5-2 over Federer after having lost their previous match in the U.S. Open final. Murray will play top-ranked Rafael Nadal, who defeated Nikolay Davydenko 6-2, 6-3.
"I have realized that I will win some and lose some,'' Federer said. "As long as I enjoy the game, I don't mind the losses. But I surely want to win the big games.''
Murray said he wants to defeat Federer when it counts.
"We had some close matches in the past. He beat me in the U.S. Open last year, but hopefully I will beat him at a Grand Slam,'' Murray said.
Federer broke Murray in the first game before dropping serve in the fifth. In the 10th game, a backhand winner from Federer and a double-fault by Murray ended the set.
In the second set, Murray broke Federer in the opening game and rallied from three game points down in the third to take a 3-0 lead. Though Murray lost serve in the sixth game, he broke back to even the match.
Federer attempted to serve and volley, but was often beaten as he approached the net.
In the third set before a crowd of 5,000, Murray broke in the third and fifth games but lost his serve in the sixth.
Federer saved three match points to rally to 6-6 in the tiebreaker, but Murray clinched it when the second-ranked Swiss star sailed a return long.
Nadal dropped his opening serve in the second game but reeled off the next six games. Davydenko hung on in the second set but was broken in the sixth game and Nadal closed out the match.
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