The Spaniard, champion here in 2009, needed to be at his resilient best to come out on top after more than four hours of top quality shot-making and thrilling rallies which earned both players a huge ovation from the Rod Laver Arena crowd.
The 19-year-old Zverev showed in spades why many consider him a future grand slam champion but was just unable to stay with the uber-fit 30-year-old in a gripping deciding set.
"Everybody knows how good Alexander is, he's the future of our sport and the present too," said Nadal, who reached the fourth round for the 10th time in 12 appearances at Melbourne Park.
"Today was a great battle, I am very happy to be through. It was an important result for me as I've lost my last couple of matches in the fifth."
Returning to Melbourne Park as ninth seed after curtailing his 2016 season because of injury, Nadal will next face Gael Monfils of France as he bids for a 15th grand slam title.
While Zverev's performance reinforced his position in the vanguard of generation next, Nadal confirmed that he is healthy enough to take advantage of the early exit of 2016 champion Novak Djokovic from his half of the draw.
It was the younger man, however, who got off to the quicker start, grabbing a break in the opening game with a sumptuous backhand dropshot and moving the former world number one around the court.
Zverev had a 20 kph advantage over Nadal on first serve but the German was unable to dominate in the second set the way he did in the first and a single break evened up the contest.
The third set developed into a ding-dong battle with neither player able to snare a single break point and it was Zverev who edged the tiebreak with an angled winner, again off his backhand.
Nadal grabbed the only break of the fourth set on Zverev's first service game and tied the contest up with his eighth ace, sending it into a decider.
Another early break for Nadal appeared to set him on the path to victory but Zverev was having none of it and broke back, only fading when he started cramping after a series of marathon rallies to allow the Spaniard to claim the victory.
"I'm disappointed but I know that this was a great match, That was a great fight. There's a lot of positives in this match," Zverev said.
"I think he's probably one of the fittest tennis players in the history of the game. Obviously I wanted to win. I could have won. It's disappointing."
Results:
Men
15-Grigor Dimitrov (Bulgaria) beat 18-Richard Gasquet (France) 6-3 6-2 6-4
3-Milos Raonic (Canada) beat 25-Gilles Simon (France) 6-2 7-6(5) 3-6 6-3
6-Gael Monfils (France) beat 32-Philipp Kohlschreiber (Germany) 6-3 7-6(1) 6-4
9-Rafa Nadal (Spain) beat 24-Alexander Zverev (Germany) 4-6 6-3 6-7(5) 6-3 6-2
13-Roberto Bautista (Spain) beat 21-David Ferrer (Spain) 7-5 6-7(6) 7-6(3) 6-4
Denis Istomin (Uzbekistan) beat 30-Pablo Carreno (Spain) 6-4 4-6 6-4 4-6 6-2
8-Dominic Thiem (Austria) beat Benoit Paire (France) 6-1 4-6 6-4 6-4
11-David Goffin (Belgium) beat 20-Ivo Karlovic (Croatia) 6-3 6-2 6-4
Women
22-Daria Gavrilova (Australia) beat 12-Timea Bacsinszky (Switzerland) 6-3 5-7 6-4
5-Karolina Pliskova (Czech Republic) beat Jelena Ostapenko (Latvia) 4-6 6-0 10-8
9-Johanna Konta (Britain) beat 17-Caroline Wozniacki (Denmark) 6-3 6-1
2-Serena Williams (U.S.) beat Nicole Gibbs (U.S.) 6-1 6-3
30-Ekaterina Makarova (Russia) beat 6-Dominika Cibulkova (Slovakia) 6-2 6-7(3) 6-3
Mirjana Lucic-Baroni (Croatia) beat Maria Sakkari (Greece) 3-6 6-2 6-3
16-Barbora Strycova (Czech Republic) beat 21-Caroline Garcia (France) 6-2 7-5
Jennifer Brady (U.S.) beat 14-Elena Vesnina (Russia) 7-6(4) 6-2
