Bulgarian Dimitrov also had to battle hard against Britain's Kyle Edmund, winning 6-3 6-7(3) 6-4 in two hours and 23 minutes at the Pat Rafter Arena.
Kyrgios, who will be under the home spotlight at this month's Australian Open, made 36 unforced errors against Dolgopolov but there were 27 winners too.
"As bad as it is to say, it's kind of like a tap. I can turn it on when I want to," the third seed told reporters.
"I'm feeling pretty good. I'm hitting the ball well and I'm serving really well. So the first two matches of the year, I've got through two tough three-setters," added Kyrgios, who beat compatriot Matthew Ebdon 6-7(3) 7-6(5) 6-2 in the second round.
"The only positive I can say about losing that first set (against Dolgopolov) is I'm putting myself in some pressure situations and getting some more court time out there which is good... I've got to try and maintain as much energy as I can."
Dimitrov was in control against Edmund as he took the first set but was dragged into a second-set tiebreak which the Briton edged to set up the decider.
Dimitrov, who survived two match points to beat local hope John Millman in the previous round, needed a solitary break to close out the match.
Kyrgios was joined in the last four by fellow Australian Alex De Minaur as the teenager followed up his win over Milos Raonic by beating American qualifier Michael Mmoh 6-4 6-0.
De Minaur will play unseeded American Ryan Harrison for a place in the final. Harrison was leading 7-6(6) 4-2 when Uzbekistan's Denis Istomin retired from the contest.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris and Martyn Herman)
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