The world number two put in a supremely accomplished performance against the unpredictable Australian to clinch a 7-5 6-1 6-4 victory in only an hour and 43 minutes.
Kyrgios had talked up his chances of a first competitive win over his good friend but he was given a Centre Court lesson as Murray notched up a 50th win at the All England Club.
The Scot moves through to a last-eight meeting with old rival Jo-Wilfried Tsonga having still not dropped a set.
This was the most eagerly-anticipated match of the fourth round and the first real test of Murray’s title credentials.
Kyrgios spoke about Murray in glowing terms on Sunday, joking it was “love at first sight” - although he surely would have wanted to wrap a racket around the Scot’s neck here.
They are very different characters, the shy, humble Scot and the brash Australian, but Murray knows what it is like to feel misunderstood.
Their friendship was on hold for the duration of this match, though, and Murray was well aware what a dangerous occasion it was despite his great record against both Kyrgios and Australians.
He had won all 18 previous tour-level matches against men from Down Under, including four against Kyrgios, three of them last year at the other grand slams.
Kyrgios did beat Murray at the exhibition Hopman Cup in January while he was back at the scene of his greatest win so far, when, as a little-known 19-year-old, he stunned Rafael Nadal in the same round two years ago.
The Australian, one of tennis’ few mavericks these days, warmed up for the match by watching his Davis Cup captain Lleyton Hewitt play doubles on an outside court.
Murray got his tactics spot on from the start. He mixed up the pace, using a lot of slice then amping up his groundstrokes. The drop shot was working superbly and bringing Kyrgios forward reaped its rewards time and again.
Initially the Australian matched his opponent, his huge serve getting him out of trouble whenever Murray threatened.
Kyrgios occasionally played maddeningly casual shots but was largely focused and, until 5-5, there was nothing between them.
The Scot took a page out of his coach Ivan Lendl’s book by hitting a short ball straight at Kyrgios, much to the 21-year-old’s amusement.
But Murray began the next game with two fizzing cross-court backhands and forced three set points. Kyrgios saved two but netted a volley on the third.
The world number two insisted after his third-round win over John Millman that Novak Djokovic’s shock exit would make no difference to him unless he made the final.
But, given the last time he reached a slam final and did not play the Serbian was here in 2012, it would surely be difficult for him not to feel his chances of a second title had improved.
If that was the case, though, it appeared to have imbued him with even more confidence rather than added pressure.
The 29-year-old forced another break of serve in the fourth game of the second set to lead 3-1, and at that point Kyrgios lost his cool.
Waiting to receive a serve from Murray, Kyrgios loudly repeated the word ‘Wow’ to himself several times and then smashed a return angrily wide. He was broken again in the next game and Murray swiftly clinched the set.
Kyrgios refocused for the start of the third but Murray was now playing at a ridiculously high level and there was nothing the 15th seed could do to prevent his opponent breaking serve again to lead 2-1 in the third set.
It was perhaps not surprising that Kyrgios was unable to sustain his level of the first set given how much tennis he has played.
This was his fourth consecutive day of action, with his matches against Dustin Brown and Feliciano Lopez both affected by rain while Murray had the luxury of the Centre Court roof.
There was no doubt he was trying, and he hit a ball out of the court attempting to return a Murray lob.
But Kyrgios could not find any answer to Murray’s brilliance and, although he saved two match points, Murray took his third with an ace.
More to follow...