Svitolina, the 28th seed, followed up her shock win over world number four Jasmine Paolini in the third round with a 6-4, 6-1 victory over the world number 75 on Rod Laver Arena.
It put her into the last eight at Melbourne Park for a third time, but her first since 2019.
“That was a lifetime ago,” said Svitolina after wrapping up the match in 1hr 23min.
“You know, so many things happen — having a daughter, Sky, then surgery as well. I’m really pleased with the performance throughout this tournament.”
Svitolina refused the usual net pleasantries between players during the match, as is the case for all Ukrainian players because of the war in their homeland.
Organisers displayed a notice on giant centre court screens explaining to spectators that no handshake would take place and asking for “respect in these difficult circumstances”.
Kudermetova raced into a 4-1 lead with a double break at the start, but that was as good as it got for her.
Svitolina, who roared back from a set down against Paolini in round three, showed her fighting qualities again to recover the deficit and lead 5-4.
