Spaniard Nadal won 6-3, 3-6, 7-6(6), 7-6(4) in front of a packed crowd at the Rod Laver Arena to move one step closer to a record-equalling 20th Grand Slam title.
"It was a very tough match," Nadal told former World No. 1 John McEnroe in an on-court interview as quoted by the ATP Tour website after the match.
"In the beginning I was in control, but you're never in control against Nick. When I made the mistake on serve in the second set, with one serve of mine, it was so difficult to break him again.
"I did the same in the fourth set, but he played a good game. I played a scary game at 5-4, it's part of the sport and you have to accept it. I tried to recover mentally for 6-5 and then the tie-break. When he plays like today with a positive attitude, he gives a lot to the sport. He's one of the best talents on Tour and I like the Nick Kyrgios of this tournament."
Nadal held serve to love nine times and landed 64 winners to reach his 12th quarter-final at Melbourne Park after three hours and 38 minutes.
The Spaniard has reached five Australian Open finals, lifting the trophy in 2009 and will now meet Dominic Thiem for a place in the semi-finals.
"It will be tough, we know each other very well," said Nadal, when asked about facing Thiem.
"He's a great character and a tough competitor. I will need to play at my best, but I feel I am moving in the right direction. I played well against Pablo two days ago and again tonight against one of the best tennis players in the world. I hope to keep going," he concluded.
( With inputs from IANS )