Meanwhile, third seed Grigor Dimitrov beat Andrey Rublev 6-3, 4-6, 6-4, 6-4, and women's fourth seed Elina Svitolina eased past 15-year-old fellow Ukrainian Marta Kostyuk 6-2, 6-2 in Melbourne.
Andreas Seppi overcame Ivo Karlovic in a five-set contest that lasted almost four hours, with the Italian eventually winning 6-3, 7-6 (4), 6-7 (3), 6-7 (5), 9-7.
All the stats and scores from the day's action can be found at the Australian Open's official website.
Nadal set the tone early on against Dzumhur with some powerful and ruthless play, per Eurosport UK:
It wasn't until 5-0 that a pair of unforced errors from the Spaniard allowed his opponent a way in, with Dzumhur finally able to hold serve and escape a bagel thanks to a superb forehand winner down the line.
Nadal, who hit a 150 mph forehand winner of his own, emerged on top after a flurry of breaks early in the second set and he soon had a commanding lead in the contest.
Meanwhile, the Open's official Twitter feed provided analysis of the 31-year-old's return stances:
The third set proved as straightforward as the first, with Dzumhur providing little in the way of resistance.
There were just two breaks of serve in the entirety of the three hours and 51 minutes that Seppi and Karlovic shared the court, with both coming for the former in the first and fifth sets.
Remarkably, Karlovic hit 52 aces during the course of the match. Per Record's Jose Morgado, the Croatian has form in this area:
Dimitrov and Rublev displayed a much lower quality of serving in their match, with the pair producing 15 and 13 double-faults, respectively, and there were 10 breaks of serve over the four sets.
Kostyuk enjoyed a sensational start to her match with Svitolina as she broke the fourth seed, eight years her senior, in the opening game.
However, the younger Ukrainian's inexperience quickly became apparent as Svitolina regained her composure, per First Post's Nikhila Makker:
Svitolina eased to the same scoreline in the second set as Kostyuk struggled to keep up.
She will take on qualifier Denisa Allertova in the next round.