
The Russian world No 2 and title favourite served out a 7-6 (7/1), 6-4, 4-6, 6-2 win over the 115th-ranked Kyrgios in two hours, 58 minutes.
It was a madhouse inside Rod Laver Arena with unpredictable Kyrgios dealing out all his assortment of unplayable serves and tweeners before a partisan home crowd, while embroiled in a running battle with the chair umpire.
But calculating Medvedev dealt with it all to ease through and will now face Dutchman Botic van de Zandschulp in the third round.
Medvedev was not happy with some of the antics of the vociferous crowd.
“I came to win this match and I am happy that I was able to do,” he said on court.
“It’s not your choice when you get booed between first and second serves, it’s not easy, I just had to stay calm.”