Karen Khachanov, a strapping 6ft 6in Russian who had beaten Tomas Berdych and John Isner in his previous two matches, was no match for Murray, who won 6-3, 6-4, 6-4 to earn a quarter-final meeting with either Kei Nishikori or Fernando Verdasco.
Khachanov matched Murray for power on a sunny Court Philippe Chatrier but was second-best in every other department as the 30-year-old world number one mastered him 6-3 6-4 6-4 to reach the quarter-finals at Roland Garros for the seventh time.
Murray will next play eighth-seeded Japanese Kei Nishikori, who recovered to beat Fernando Verdasco of Spain 0-6, 6-4, 6-4, 6-0 in the fourth round. "Each match I feel like I played better", said Murray, who lost in last year's final.
McEnroe, too, was full of praise for the No 1, although he is not so sure that Murray was so far below his peak when he arrived in Paris.
But boosted by the return of coach Ivan Lendl to his player's box, Murray's form has surged - with his third-round defeat of Juan Martin del Potro suggesting he could go deep in Paris.
Murray finished five aces and a total of 29 winners.
He added with a smile: "I mean, always, you know, when we play, it's always a battle". I think we were both very tense.
And each time, the less-accomplished player won.
Murray played cleanly to beat 53rd-ranked Karen Khachanov of Russian Federation 6-3, 6-4, 6-4 on Court Philippe Chatrier.
Asked in an interview with Eurosport if his daughter was showing any interest in tennis, Murray said: "I think she kind of recognises me when I'm on the TV".More news: Proteas dissect fragile Sri Lanka
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Svitolina rallied to beat Croatian qualifier and world No. 290 Petra Martic 4-6, 6-3, 7-5 on Court Suzanne Lenglen.
"I said after the last match that what's important is what you're thinking right before the following point".
'Actually I'm very bad with the memories, ' he said when asked about their meeting past year.
"After that (first set) I started playing with fewer errors and that was good".
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.
Third-seeded Simona Halep advanced to the quarterfinals by beating No. 21 Carla Suarez Navarro 6-1, 6-1. Marin Cilic completed the quarter-final line-up when South Africa's Kevin Anderson retired with a thigh injury trailing 6-3, 3-0.
The only break of serve in the opening set came in the sixth game.
Murray said: " He was pumped, he was happy with how I played.