He fired 34 winners and didn't face a single break point in his one-hour, 49-minute win over the highly-rated wildcard.
Kyrgios, the 29th seed and bidding to add a first French Open last 16 place to his runs to the 2014 Wimbledon and 2015 Australian Open quarter-finals, wasn't helped by requiring a medical timeout for an elbow injury late in the second set against Murray.
Murray, who fired 12 aces and 45 winners while Kyrgios was undone by 37 unforced errors, goes on to face unseeded Frenchman Jeremy Chardy, who surprised 17th-seeded Belgian David Goffin 6-3 6-4 6-2.
Chardy is the fourth Frenchman to make the last 16.
It was 28-year-old Murray's third successive win over Kyrgios, all without dropping a set, as he took his record on clay this year to 13-0.
"I used variety and slice, tried to mix it up to break his rhythm and it seemed to work," said Murray, who said he knew Kyrgios wasn't serving at his full power as the match progressed.
"At the beginning he was serving big, over 200 kilometres an hour, and then started slowing down to 170, 180, and not really going for aces."
Kyrgios, who knocked Rafael Nadal out of Wimbledon last year and beat Roger Federer in Madrid this month, said Murray was a different proposition.
"Andy is one of the best defenders at the moment," he said.
"But I wasn't near 100 per cent per cent today."
Marin Cilic, the ninth-seeded US Open champion, continued his quiet progress to reach the fourth round for the third time.
The 26-year-old eased past Leonardo Mayer, the Argentine 23rd seed, 6-3 6-2 6-4 and will take on either 2013 runner-up David Ferrer or Simone Bolelli for a quarter-final slot.
Cilic has dropped serve just once in 40 games so far.
-AAP
