Australians have not toasted a home-grown champion since Mark Edmonson in 1976 and the 17th seeded Kyrgios was the last remaining hope. The 22-year-old, who has vowed to banish his bad boy behavior, beat Dimitrov earlier in January on his way to taking the ATP tournament in Brisbane.
But it was Dimitrov who drew first blood in their last 16 clash. He claimed the first set tiebreak seven points to three. And the 26-year-old Bulgarian seemed on course to take a grip of the match when he served for the second set leading 5-4.
But to the cheers of the partisans, Kyrgios levelled at 5-5 but again faltered in the tiebreak.
He claimed the third 6-4 to offer some hope and showed his fighting spirit when he broke Dimitrov when he was serving for the match in the fourth set.
However he could not capitalise on the reprieve and slumped in the tiebreak.
"Playing against Nick is always tricky, two weeks I lost against him," Dimitrov said. "He was serving and playing unbelievable and he fought really hard. It's one of those matches that you have to be locked in and try to get any opportunity you have.
"Even when I was serving for the match I felt that I was not finding my spots very well and I'm just glad I got through that match."
Dimitrov will next play the unseeded Briton Kyle Edmund who reached his first Grand Slam quarter-final following a four set win over the veteran Italian Andreas Seppi.
With his victory, he became only the sixth British man to reach the quarter-finals of the Australian Open since tennis was opened up to professionals in 1968.
"It's a good feeling,” said the 23-year-old. “It was a really interesting match. It was a very close first set, he was hitting the ball very clean and dictating a lot of the points.
"But after I broke him in the second set I really feel like I took the momentum.
"He was playing really well but so was I. I'm through to my first quarter-final and I'm very happy."