Murray beat the Serbian world number two 7-5 7-5 in exactly two hours on Wimbledon's Centre Court and is now guaranteed at least a silver medal.
Standing between the Briton and the biggest title of his career is Federer, who beat him in the Wimbledon final.
The Swiss overcame Juan Martin del Potro 3-6 7-6 (7-5) 19-17.
The match lasted four hours and 26 minutes, the longest three-set singles match in the Open era.
"It was a big match obviously. Very tough from start to finish," said Federer, who won his seventh Wimbledon singles title at the Olympic venue just a few weeks ago.
"I don't think I have ever played as long a set in a best of three-set match, so it was very physical at the end and so mental.
"I feel bad and horrible for Juan Martin but he can be very proud."
Federer struggled in the windy conditions on Centre Court and was broken in game eight of the first set, which Del Potro served out to love.
After failing to convert two break points early in the second, the top seed scrambled his way out of trouble in games five and nine before taking the set on a tie-break.
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