Having lost the first set, Murray responded by claiming a double break in the second, but Federer fired back and won six of the final seven games to seal an impressive 6-3 7-5 quarter-final victory and even up their head-to-head record at 11 wins apiece.
The Briton had been hoping to make an impression in Cincinnati with the US Open just around the corner, but it is Federer who looks imperious heading into Flushing Meadows in under two weeks.
Federer, who won the last meeting between the pair at the Australian Open earlier this year, made a barnstorming start although Murray soaked up the pressure by saving six break points in his opening two service games.
However, from 30-0 up at 2-2, Murray contrived to lose his serve with a forehand wide handing Federer a deserved break for his persistence at the seventh opportunity.
The Swiss was uncharacteristically sloppy immediately afterwards but managed to stave off a couple of break points and ruthlessly went on to break a listless Murray once more to close out the set 6-3.
Federer started sluggishly in the second set, though, and a couple of errors opened the door for Murray, whose forehand winner gave him three break points before he finally penetrated the 33-year-old's serve at the third attempt.
Another break followed in the fifth game as Federer tamely sent a backhand into the net to give Murray a 4-1 lead.
Any thoughts Murray may have had of taking the match to a decider were put on the back-burner as Federer immediately got one of the breaks back and the Scot's serve was mercilessly exposed once again as a double fault levelled things up at 4-4.
Federer made it four games on the trot by holding serve although Murray recovered from the blip to halt his opponent's surge.
However, having to hold once more to take the set to a tie-break, Federer was clinical and showed all of his experience, setting up match point with a daring drop shot which allowed him a simple backhand winner.
Murray, whose first serve was at a lowly 48 per cent, then sent a forehand return into the net to hand Federer victory and a semi-final clash with Canadian fifth seed Milos Raonic.
Murray was left to ponder what might have been had he taken his numerous opportunities to break Federer's serve.
He told atpworldtour.com: "I started the match off pretty slow tonight.
"[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 was well up in the second and blew it. It's a shame."