Having lost the first set, Murray reacted with a double break in the second only for Federer to fire back and win six of the final seven games to seal a 6-3 7-5 quarter-final victory and even up their head-to-head record at 11 wins apiece.
The British number one had a chance to make an impression in Cincinnati with the US Open just around the corner, but Federer is the man going into Flushing Meadows in under two weeks on a high.
"I started the match off pretty slow tonight," Murray is quoted as saying by Sky Sports News.
"[Federer] came out quick. Then I had a couple break points in back-to-back games to get into it in the first set. I didn't get either of them.
"Then obviously I was well up in the second and blew it. It's a shame."
Federer will now face Milos Raonic for a place in the final.