The 16-time Grand Slam champion defeated the 28th seed Dzumhur 6-1, 6-3, 6-1 and will play Argentina's Diego Schwartzman next.
The Spanish world number one showed no mercy to 28th seed Damir Dzumhur on Margaret Court Arena, as he rediscovers his best form after ankle trouble.
The top seed raced through the match in just 1hr 50min, wasting as little energy as possible in the 6-1, 6-3, 6-1 rout.
"I was very, very focused," Nadal said. "I'm very happy with everything and to have another chance on Sunday."
That chance will be against 24th seeded Argentine Diego Schwartzman for a place in the quarter-finals.
Dimitrov gets back on track
Also, World number three Grigor Dimitrov got his Australian Open back on track Friday with a gutsy win on another searing day, as organisers defended the tournament heat policy.
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."
Cilic ousts Harrison
Former US Open champion Marin Cilic reached the last 16 for the first time in seven years with a straight sets win over Ryan Harrison on Friday.
The Croatian sixth seed was too strong for the 45th-ranked American, winning 7-6 (7/4), 6-3, 7-6 (7/4) in 2hr 29min in a night match on Hisense Arena.
Cilic, last year's beaten Wimbledon finalist, will face Spanish 19th seed Pablo Carreno Busta in Sunday's fourth round.
He broke Harrison's serve twice, hit 53 winners and was solid on his own serve.
Cilic is coming off an outstanding 2017 where he lost to Roger Federer in the Wimbledon final and made the quarter-finals at Roland Garros along with climbing to a career-high ranking of four.
Kyrgios topples idol Tsonga
Australia's Nick Kyrgios won an electric four-setter with his idol Jo-Wilfried Tsonga to advance to the round of 16.
The 17th seeded Kyrgios needed three tiebreakers to win a crunch match with the former finalist 7-6 (7/5), 4-6, 7-6 (8/6), 7-6 (7/5) in 3hr 17min in a spectacular night match on Rod Laver Arena.
It pitches the volatile Australian into a round of 16 showdown with Bulgaria's world No.3 Grigor Dimitrov on Sunday.
Kyrgios, urged on by his home crowd, traded breathtaking volleys with Tsonga, who lost to Novak Djokovic in the 2008 Australian final when Kyrgios was a 12-year-old fan.
"It was amazing. I've never won a match on this court before but playing Jo I was obviously very nervous," Kyrgios said on court.
"He was a guy I looked up to as a kid, still do, he's a great guy. I'm just so happy to get through.
"I was getting prepared for a fifth set in that (fourth set) tiebreaker.
"I thought he was going to hit two big first serves and I was in a lot of trouble but I stayed composed, tied to make some returns and fight it out."
Svitolina keeps her dreams alive
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 Elise 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.
Wozniacki into last 16
World number two Caroline Wozniacki kept her bid for a first Grand Slam title on course as she stormed into the last 16 on Friday.
The second seed only scraped through to the third round by the skin of her teeth, saving two match points at 5-1 down in the third set against 119th ranked Jana Fett.
But on Friday she gave her most assured performance of the tournament so far, cruising past Kiki Bertens of the Netherlands 6-4, 6-3 in an hour and 26 minutes.
She next faces 19th seed Magdalena Rybarikova of Slovakia for a place in the quarter-finals.
No matches have been called off or roofs closed at the opening Grand Slam of the year despite the soaring temperatures, with tournament organiser Craig Tiley defending the decision.
"These are professional athletes," he said.
"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."
Organisers only activate the extreme heat policy 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 joined Nadal in the round of 16, overcoming the elements in a fighting five-set win over Nikoloz Basilashvili and will next play Italian Andreas Seppi who won a battle of the veterans against Croatia's 38-year-old Ivo Karlovic.
Spanish 10th seed Pablo Carreno Busta, a semi-finalist at last year's US Open, also marched on.
Despite being the second seed, Caroline Wozniacki has not impressed so far.
She is the late match on Rod Laver Arena against Dutch 30th seed Kiki Bertens and will play 19th-seeded Slovak Magdalena Rybarikova if she wins.
- Kyle Edmund (GBR) bt Nikoloz Basilashvili (GEO) 7-6 (7/0), 3-6, 4-6, 6-0, 7-5
- Pablo Carreno-Busta (ESP x10) bt Gilles Muller (LUX x23) 7-6 (7/4), 4-6, 7-5, 7-5
- Grigor Dimitrov (BUL x3) bt Andrey Rublev (RUS x30) 6-3, 4-6, 6-4, 6-4
- Diego Schwartzman (ARG x24) bt Alexandr Dolgopolov (UKR) 6-7 (1/7), 6-2, 6-3, 6-3
- Andreas Seppi (ITA) bt Ivo Karlovic (CRO) 6-3, 7-6 (7/4), 6-7 (3/7), 6-7 (5/7), 9-7
- Rafael Nadal (ESP x1) bt Damir Dzumhur (BIH x28) 6-1, 6-3, 6-1
- Nick Kyrgios (AUS x17) bt Jo-Wilfried Tsonga (FRA x15) 7-6 (7/5), 4-6, 7-6 (8/6), 7-6 (7/5)
- Marin Cilic (CRO x6) bt Ryan Harrison (USA) 7-6 (7/4), 6-3, 7-6 (7/4)
- Petra Martic (CRO) bt Luksika Kumkhum (THA) 6-3, 3-6, 7-5
- Denisa Allertova (CZE) bt Magda Linette (POL) 6-1, 6-4
- Elise Mertens (BEL) bt Alize Cornet (FRA) 7-5, 6-4
- Elina Svitolina (UKR x4) bt Marta Kostyuk (UKR) 6-2, 6-2
- Magdalena Rybarikova (SVK x19) bt Kateryna Bondarenko (UKR) 7-5, 3-6, 6-1
- Carla Suarez (ESP) bt Kaia Kanepi (EST) 3-6, 6-1, 6-3
- Anett Kontaveit (EST x32) bt Jelena Ostapenko (LAT x7) 6-3, 1-6, 6-3
- Caroline Wozniacki (DEN x2) bt Kiki Bertens (NED x30) 6-4, 6-3