Men's third seed Grigor Dimitrov also booked his spot in the fourth round as he downed Andrey Rublev in four sets, while Great Britain's Kyle Edmund beat Nikoloz Basilashvili 7-6 (0), 3-6, 4-6, 6-0, 7-5.
In the women's draw fourth seed Elina Svitolina brushed aside 15-year-old Marta Kostyuk in just under an hour, and Belgium's Elise Mertens beat Alize Cornet 7-5, 6-4.
Read on for a closer look at the Day 5 action.
(1) Rafael Nadal bt. (28) Damir Dzumhur: 6-1, 6-3, 6-1
(3) Grigor Dimitrov bt. (30) Andrey Rublev: 6-3, 4-6, 6-4, 6-4
Kyle Edmund bt. Nikoloz Basilashvili: 7-6 (0), 3-6, 4-6, 6-0, 7-5
(4) Elina Svitolina bt. Marta Kostyuk: 6-2, 6-2
Carla Suarez Navarro bt. Kaia Kanepi: 3-6, 6-1, 6-3
Full results can be found at the Australian Open's official website.
Nadal blew Dzumhur away in an opening set that lasted just 22 minutes. Two breaks of serve saw the Spaniard 5-0 ahead in a flash, and although Dzumhur did finally get a hold on the board, he could do nothing to stop Nadal serving out to go a set ahead.
Another break from the top seed saw him 2-0 ahead at the start of the second set, but Dzumhur managed to draw level at 2-2 with a break of his own, sealing it with a fine backhand passing shot after pulling Nadal to the net.
It was an excellent response from the Bosnian as he proved he could cause problems for his auspicious opponent but Nadal regained the initiative immediately as he broke straight back.
The second set was a much more competitive affair than the first had been as Nadal's level dropped slightly and Dzumhur upped his game.
However, proof of Nadal's superiority showed in his ability to continue to win games with percentage play, and he broke again to seal the second set.
The 16-time Grand Slam winner then took 10 minutes to hold his serve in the first game of the third set before again breaking Dzumhur at the first time of asking for a 2-0 lead, a brilliant pick-up earning him the crucial lead after a delicate drop-shot.
From there the match was effectively over and, after another break, Nadal served for the match and sealed the win with an ace on his third match point, per Eurosport UK:
Teenager Kostyuk had caught the eye in becoming the youngest player since 1997 to reach the third round of a Grand Slam, but she caused Svitolina few problems in their clash on the Rod Laver Arena.
The two Ukrainian players competed for just 59 minutes before the world No. 4 booked her spot in the fourth round.
Svitolina's first-serve percentage of 71 compared to Kostyuk's paltry 37 proved the difference as the 23-year-old claimed five breaks of serve in the match.
Per BBC Sport, Kostyuk took an admirable attitude to her defeat after an impressive tournament: "[I learned] a lot. How much do you have to pay Svitolina to have a one-hour lesson? I got it for free."