The 25-year-old tennis player from Russia (fifth seed) defeated Dane Holger Rune (ninth) in five sets with a score of 6:3, 3:6, 6:3, 4:6, 7:6.
The game lasted 3 hours 39 minutes.
Rublev's next opponent will be the winner of the match between Serbian Novak Djokovic and Alex de Minor from Australia.
The Australian Open has a total prize pool of over $51 million.
At the Grand Slam tournaments, the Russian did not go beyond the quarterfinals.
Earlier it was reported that the quarterfinal pairs of the Australian Open in the women's category were determined.