Dimitrov downed the 17th seeded Kyrgios 7-6 (7/3), 7-6 (7/4), 4-6, 7-6 (7/4) in 3hr 26min and will face Britain's Kyle Edmund in the quarter-finals on Tuesday.
Dimitrov stepped up his campaign after a couple of indifferent wins in the earlier rounds to avenge his defeat to Kyrgios in the semi-finals of this month's Brisbane International.
He won all three tiebreakers in a charged night match atmosphere on Rod Laver Arena before a capacity home crowd willing their player on.
"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.
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"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."
Kyrgios double-faulted to lose the opening set tiebreaker and was broken in the seventh game of the second set leaving the moody Australian to shake his head cussing at the changeover and uttering "embarrassing."
It was the Bulgarian's greater poise and depth of shot that carried him through with Kyrgios frequently missing the lines.
The Australian broke early in the third set in his do- or-die bid to stay in the match and took the set with an ace.
But Dimitrov got a crucial service break in the eighth game of the fourth set when Kyrgios put a smash into the net to allow the Bulgarian to serve out for the match.
The unpredictable Australian managed to break back to force a third tiebreaker.