He will next face either Australia's 17th seed Nick Kyrgios or former victor Jo-Wilfried Tsonga of France for a place in the quarter-finals.
The Bulgarian won 6-3 4-6 6-4 6-4 in high temperatures on Rod Laver Arena.
His unrestrained joy upon winning showed his relief at finally putting Rublev away in the topsy-turvy contest.
"These are most important matches when things are not working and I am able to find a way", Dimitrov, 26, said.
Petra Martic of Croatia celebrates winning against Luksika Kumkhum of Thailand
"He's a good player".
On the other hand, Rublev gave his best to stay in touch as long as possible, ripping his forehands to move Dimitrov from the comfort zone, and he had the opportunity to extend the match if he had broke Grigor in the last game of the match when Bulgarian served for the win. "He beat me at the US Open so I knew what to expect and what I had to do". A strong hold followed from Dimitrov, who saved two breakpoints in the final game before taking the match.
Dimitrov, the reigning ATP finals champion, committed 61 unforced errors, but he earned his first win over Rublev in the second career matches.
The third set proved to be a role reversal of the second, as four games on the spin helped Dimitrov recover from 4-2 down to take command of the tie.
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