The big-hitting Khachanov had beaten Tomas Berdych and John Isner en route to a maiden last-16 grand slam appearance, but world number one Murray's game was an altogether different task and the Briton emerged a deserved 6-3 6-4 6-4 victor.
He proved too experienced for Karen Khachanov, defusing the power of the 21-year-old Russian to win 6-3 6-4 6-4.
- Murray voices his support for those impacted by the terror attacks in London and Manchester which left 29 people dead and scores injured.
"Obviously there was bad tragedy in London and Manchester".
"He was pumped", Murray said.
"Paris has had some problems in the last few years and I'm sure everyone will join me in sharing the fact that our thoughts and prayers are with those affected by this".
"I am grateful I can come out and perform in front of you".
Rohan Bopanna and his Canadian partner Gabriela Dabrowski stormed into the semi-finals of the mixed doubles event of the French Open with a straight-set upset win over the duo of Sania Mirza and Ivan Dodig of Croatia here yesterday.
Thiem has motored through the first four rounds to reach just his second Grand Slam quarter-final, but the challenge is about to get much tougher for one of the game's rising stars.
"I think Andy's been great", McEnroe said. "I'm going to be ready for that".
Qatar row: Trump claims credit for isolation
Saudi Arabia and the UAE have now drawn the line and appear determined to subdue Qatar , he added. "We are friends. Qatar is the third largest market for Thai products in the Gulf Cooperation Council (GCC) countries.
After arriving at Roland Garros with expectations tempered by a season of struggle so far, Murray has played himself into form nicely.
Murray has an excellent record against Nishikori, but will still have vivid memories of the defeat he suffered at last year's US Open.
The British-Brazilian pair looked in control of the match and Murray served for the victory in the second set.
"I think he started really well, especially as the court's bounce was really high today and he was using very heavy forehand", he said of the match.
Wawrinka has prevailed all five times they've played on clay, including a 2008 clash in Paris.
"I sill feel the ankle some times but I am able to run".
Later Monday, Czech world No. 2 Karolina Pliskova, also in the running to become both a first time major victor and the new world No. 1, took on Veronica Cepede Royg in her last-16 tie.
However, Martic, bidding to become only the 10th qualifier to make the last eight in Paris threw away a golden chance for victory. Paris has had some problems in the past year or two.
Third seed and 2015 champion Stan Wawrinka made the last eight defeating Gael Monfils 7-5, 7-6 (7), 6-2.
The two compatriots have been involved in a recent feud over the Fed Cup and are barely on speaking terms. Conditions were hard. It was pretty windy out there.