The third seed had plenty to prove after a huge second-round fright from a qualifier, who pushed him to five sets.
And the Bulgarian delivered in a testing 6-3, 4-6, 6-4, 6-4 win over Russian rising star Andrey Rublev on Rod Laver Arena as temperatures touched 40 Celsius (104 Fahrenheit).
“These are the most important matches for me, when things are not working for me and I find a way,” he said. “I’m feeling good physically, the heat didn’t scare me at all today, so that’s a good sign.”
He will next face the winner of an intriguing night match which pits Australian Nick Kyrgios against French veteran Jo-Wilfried Tsonga.
Fourth seeded woman Elina Svitolina also kept her title dreams alive by ending the hopes of young teenage pretender Marta Kostyuk.
At just 15, Kostyuk was the youngest Melbourne Park third-round contestant since Martina Hingis in 1996, and was hailed after her previous win as “the future of tennis.”
But she still has a lot to learn with fellow Ukrainian Svitolina handing out a 6-2, 6-2 lesson.
“She’s definitely got a bright future,” said Svitolina, adding: “It’s very special for me to get past the third round.”
She next plays another qualifier — big-serving Czech Denisa Allertova who romped past Magda Linette 6-1, 6-4 — for a place in the quarter-finals on Sunday.
In a tournament shorn of seeds, 81st ranked Petra Martic also swept into the round of 16, celebrating her 27th birthday by holding off a gritty three-set challenge from Thai qualifier Luksika Kumkhum.
Her reward is a match against Belgium’s Elize Mertens, who beat struggling Alize Cornet of France in two tough sets.
Cornet was among players wilting in the heat, with a doctor taking her blood pressure early in the second set as she succumbed to the baking weather.
No matches have been called off at the opening Grand Slam of the year despite the soaring temperatures, with tournament organizer Craig Tiley defending the decision.
“The policy is from consultation with the players,” he said. “These are professional athletes.
“We are at the end of the day an outdoor event. We want it to stay an outdoor event as long as possible but at the same time ensuring that the health and wellbeing of players is taken care of.”
Organizers only active the extreme heat policy and halt play or close roofs when the temperature exceeds 40 Celsius and the wet bulb globe temperature index hits 32.5 Celsius.
On Thursday, Novak Djokovic described the conditions as “brutal,” complaining it was hard to breathe.
Kyle Edmund was the first man to reach the round of 16, overcoming the elements in a fighting five-set win over Nikoloz Basilashvili.
He is the only British man in the main draw after Andy Murray’s injury withdrawal and will play either Croatia’s 38-year-old Ivo Karlovic or Italian Andreas Seppi next.
Spanish 10th seed Pablo Carreno Busta, a semifinalist at last year’s US Open, also marched on, beating Gilles Muller.
Rafael Nadal faces a stiff challenge later on Margaret Court Arena when he takes on 25th ranked Damir Dzumhur, the first seed he has played in his comeback from a knee problem.
The Spanish world number one has so far been dominant in his search for a 17th Grand Slam title.
Despite being the second seed, Caroline Wozniacki has not impressed so far, needing to save two match points and rally from 5-1 down in an epic third set against little-known Jana Fett in round two.
She is the late match on Rod Laver Arena against Dutch 30th seed Kiki Bertens and will play 19th seeded Slovak Magdalena Rybarikova is she wins.