Having started the French Open harbouring significant doubts about his form, Briton Murray has played himself into familiar territory.
He proved too experienced for Karen Khachanov, defusing the power of the 21-year-old Russian to win 6-3 6-4 6-4.
Next up for Murray is a rerun of his US Open quarter-final with Kei Nishikori, which the Japanese won, and third seed Stan Wawrinka is likely to be waiting if he can get through that.
It appears a dramatic turnaround for Murray, who arrived at Roland Garros having lost back-to-back matches against Borna Coric and Fabio Fognini.
But former Wimbedon, US Open and Australian Open champion McEnroe said: “I don’t think he was as far away as people were saying. It’s a matter of attitude.
“He’s tougher to beat in the slams and I think he’s proving that now.
“The draw looked fairly tough in the beginning, but now you’d have to say you’d be somewhat surprised if he didn’t get to the semis if not the final.”
Russian Khachanov was the youngest man to reach the fourth round at Roland Garros for eight years, and he showed enough in this match alone to suggest he will be going a lot further in the not-too-distant future.
He has the swagger of youth, a serve befitting his 6ft 6ins and a forehand that helped him to 34 winners.
But there were 38 unforced errors, too, compared to just 14 for Murray, who kept his shots deep from the start to prevent Khachanov stepping into the court, and defended brilliantly.
It was Murray at his best as he scampered around the back of the court on break point at 3-2 in the first set, retrieving the seemingly irretrievable until Khachanov, ranked 53, pushed a forehand wide.
The Scot could never quite get rid of his opponent, a sloppy service game in each of the second and third sets allowing Khachanov to retrieve early breaks.
But Murray stepped up again immediately both times and served out the win in two hours and four minutes.
He used his post-match interview to send his condolences to the people caught up in Saturday’s terror attack in London.
He said: “It was a terrible tragedy in London, also in Manchester. Paris has also had some problems in the last one or two years.
“I’m sure everybody will join me in sharing thoughts and prayers for everyone who’s been affected by this. It’s obviously something affecting large parts of Europe and all over the world.
“I appreciate everyone still coming out to support the tennis and creating a fantastic atmosphere.”
Khachanov had beaten Tomas Berdych and John Isner to make the last 16, but Murray went into the match buoyed by his third-round win over Juan Martin del Potro.
He felt he stepped up another level against Khachanov, saying: “I think this was probably the best I have played overall. It was difficult conditions. It was pretty windy out there. Wasn’t easy. But each match I feel like I played better. I have hit the ball cleaner and started to see the right shots at the right moments. I’ve come a long way the last 10 days or so.”
Nishikori recovered from losing the opening set 6-0 to Fernando Verdasco to win 0-6 6-4 6-4 6-0.
Third seed Wawrinka is yet to drop a set and ended France’s hopes for another year with a 7-5 7-6 (9/7) 6-2 victory over Gael Monfils.
In the last eight Wawrinka will face seventh seed Marin Cilic, who has breezed through the draw so far.
He did not even have to complete his match yesterday, with opponent Kevin Anderson pulling out when trailing 6-3 3-0 with a thigh injury.
Rafael Nadal and Novak Djokovic will look to set up a semi-final clash today, with Nadal taking on Carreno Busta and Djokovic meeting Dominic Thiem.
Jamie Murray and Bruno Soares suffered a disappointing loss to Santiago Gonzalez and Donald Young in the quarter-finals of the men’s doubles.
The British-Brazilian pair looked in control of the match and Murray served for the victory in the second set.
But it was Gonzalez and Young who eventually prevailed 3-6 7-6 (7/3) 7-6 (7/4).
Murray and Soares were the highest seeds left in the tournament and had harboured hopes of adding Roland Garros to their Australian and US Open trophies from last year.
But the turning point came when Gonzalez and Young broke Murray at 5-3 in the second set.