Having started the French Open harbouring significant doubts about his form, the world number one has played himself into familiar territory.
Russian Khachanov was the youngest man to reach the fourth round at Roland Garros for eight years, and the 21-year-old’s time will surely come, but Murray used his experience to win 6-3 6-4 6-4.
The Scot used his post-match interview to send his condolences to the people caught up in Saturday’s terror attack in London.
He said: “Terrible tragedy in London, also in Manchester only six or seven days ago. Paris has also had some problems in the last (few) years.
“I’m sure everybody will share in 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, ranked 53, had beaten Tomas Berdych and John Isner to make the last 16, combining the swagger of youth with a big serve and even bigger forehand.
Murray came into the match buoyed by his third-round victory over Juan Martin del Potro, where he at last began to resemble the man who conquered all before him at the end of last year.
He was on the money from the start here, keeping the ball deep and pulling Khachanov around the court.
Some classic Murray defence drew the error from Khachanov and a break for 4-2, and Murray went on clinch the first set comfortably.
There were great moments from Khachanov, particularly when he was allowed to step into the court and unleash his forehand, but this was a familiar script.
Murray is a master at frustrating young players into too many errors with his remarkable talent simply for getting balls back in play.
He broke again for 2-1 in the second set and the only real blip came three games later when Khachanov broke back.
Having only made two unforced errors until that point, Murray threw in three in one game in blustery conditions, but broke again straight away as Khachanov showed his inexperience with a poor game of his own.
This was the first time the young Russian had played a top-five opponent, and it was an invaluable lesson in the relentlessness needed to be the best.
Chess fan Khachanov began to find himself a pawn in Murray’s game as the 30-year-old moved ahead again at the start of the third set.
Khachanov was given brief hope when he levelled at 4-4 but, as in the second set, he could hold onto his subsequent service game and Murray celebrated a dominant victory with clenched fists.
It was a 650th tour-level win for the Scot, who will face either Kei Nishikori or Fernando Verdasco in the last eight.