He returns to action on Sunday night with a fourth-round clash with third seed Grigor Dimitrov.
The 49th-ranked Briton fought back to take the last two sets and win 7-6 (7/0), 3-6, 4-6, 6-0, 7-5.
He will next face Australian Nick Kyrgios who beat French veteran Jo-Wilfried Tsonga in four close and entertaining sets in a prime-time evening match on Rod Laver Arena.
"I was like, 'Man, you may as well just stay out here, they probably enjoy that more than the tennis.'" Kyrgios added.
"How I win right now, I love it", Dimitrov said after the match, as quoted on the ATP Tour website.
Fourth seed Svitolina also kept her title dreams alive by ending the hopes of young teenage pretender Marta Kostyuk.
Cornet slumped to the court after serving during the second set of her 7-5 6-4 defeat by Mertens at the Hisense Arena and needed a medical assessment as temperatures pushed past 40 degrees Celsius at Melbourne Park.
"How much you have to pay Svitolina to have one-hour lesson?"
"I think it could be risky, but I think that the fact the doctor came on the court and took my blood pressure and she was looking if I was feeling good enough to keep playing the match".
"My serve, for example, failed me, too".
No matches have been called off so far at the opening Grand Slam of the year despite the soaring temperatures, with tournament organizer Craig Tiley defending the decision. "These are professional athletes, we are at the end of the day an outdoor event".
"It is a mistake to play".
The tournament has an Extreme Heat Policy which goes into effect when the air temperature exceeds 40 Celsius and the wet-bulb reading, which takes into account other factors such as humidity, is more than 32.5 C (91 F).
The victor will be rewarded with an unseeded quarter-final opponent - either Brit Kyle Edmund or Italian Andreas Seppi, who continues to prove an Open giant-killer.
World No. 2 Caroline Wozniacki kept her bid for a first Grand Slam title on course as she stormed into the last 16 of the Australian Open yesterday.
The 6-3 4-6 6-4 6-4 victory looked comfortable enough for the 26-year-old.
Australia has waited 42 years for a new men's champion, so expectations will rise again following Kyrgios's impressive four-set win, a third successive match without a major meltdown for the hot-headed 22-year-old.
But after barely surviving the first week, the Bulgarian knows he must raise his game to get past the in-form Kyrgios and keep his Open hopes alive.