Murray, a three-time runner-up, downed the 19-year-old 6-3, 7-6 (7/5), 6-3 in 2hr 5min and will face seventh seed Czech Tomas Berdych for a place in the final.
The Scot was too composed and steady for the exciting 19-year-old and took his record over Australian players to 11-0 before a partisan home crowd.
Murray grabbed three service breaks and only conceded a service break deep in the final set to underline his dominance over the 53rd-ranked Kyrgios.
Kyrgios played at his usual high tempo and made 38 errors, 22 of them off his forehand, while winning 65 percent first serves.
"It was a tricky match in windy conditions and I tried to start as quickly as possible because I know how dangerous Nick is," Murray said.
"Against Nick he is a huge hitter of the ball so I tried to keep it out of his strike zone as much as possible, but in the wind if you can use the slice and keep the ball low it is difficult to control.
Murray reached the semi-finals of the Australian Open for the fifth time where he will take on Berdych, who holds a 6-4 winning record over the Scot.
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