Federer will face ninth-seeded Marin Cilic in the quarterfinals, while Murray will take on Jo-Wilfried Tsonga.
But this was his most serious examination yet, a proper test and a close encounter of the intense kind.
Murray got the first break of the fourth set, when Tsonga was serving at 2-3 and pushed a backhand long.
But, in the end, his experience and fitness made the crucial difference.
The crunch moments arrived at the start of the fifth set. He put us through a bit of strife but we got there in the end.
Murray has won eight of their previous 14 matches, including the last four, but none were on grass.
"At the beginning you try to work your way through and play good tennis but now you are trying to get through matches and play as well as possible and I am happy to get into the semis".
Smith said: "Andy would have known what he was looking for in his coaching team and there's no way he'd have approached Ivan if he didn't feel there was something to gain from it, and it looks already (like that's the case)". At one point, you're used to it.
"That's why it's great to have tomorrow, a day of rest and recovery".
Obviously it was a tough match.
The statistics support Murray's case.
Federer said: "It was an emotional win, always when you come back from two sets to love, but because of the season that I've had, it's wonderful".
The Scot started off as the favourite going into today's match, having decimated each of his opponents en route to the quarter-finals easily.
Three years ago Murray also cruised into the last eight but, with the hosts desperate for a first men's champion for 77 years, near hysteria broke out as the Scot edged towards glory.
Jo-Wilfried Tsonga of France falls over next to the net as he plays against Andy Murray of Britain during their men's singles quarterfinal match on day ten of the Wimbledon Tennis Championships in London, Wednesday, July 6, 2016. "But that was to his credit for just keeping cranking out serves and big returns". "There's a lot more hopes left than me".
"I'll have to have a look and see some of his matches to get an idea of maybe some of the things he does differently on the grass courts, what his strengths are, maybe some of the things he struggles with a bit".
Through: Andy Murray is into the semi-finals. Roger Federer has a 9-2 record over his semifinal opponent Milos Raonic.
In fact, since 31-year-old Tsonga defeated the British star at the 2008 Australian Open, Murray has racked up 26 successive wins over French opponents.
Federer saved three match points and battled back from two sets down on Centre Court to beat Cilic 6-7 (4/7) 4-6 6-3 7-6 (11/9) 6-3 in the contest of the tournament so far. "He has been to the final here, beaten Djokovic and Federer at Wimbledon and is very very good", said Murray.
And when the match was tied at two sets all, the juggernaut of Murray support seemed as though it might be prematurely derailed.
Rafael Nadal did not play in the tournament because of a wrist injury and Novak Djokovic bowed out in round three, leaving Andy Murray and Roger Federer as the top two title favorites heading into the second week.
But just when the match appeared to be spiralling out of control for the agitated Scot, the 2013 champion rediscovered his early authority to dominate the decider and set up a semi-final with Czech 10th seed Tomas Berdych.