Played under a closed roof in Rod Laver Arena, the Spaniard looked strong throughout against his plucky opponent as he set up a clash against France's Gael Monfils.
After a third straight day of temperatures soaring over 40 degrees Celsius, the extreme heat policy was fully implemented for the first time, much to Nadal's delight.
"I was very happy to see the roof out there today," Nadal told reporters.
"But it was still very humid and still very hard conditions even with the roof on for that match. I felt that I was ready."
Three days before the tournament began, Kokkinakis interviewed Nadal as part of a sponsor's event, quizzing him on a number of topics.
Nadal enjoyed the light grilling but said the Australian might not be cut out for a job in journalism just yet. "My advice is keep working on tennis," he said, with a smile.
Nadal was, however, impressed by Kokkinakis's tennis ability and predicted a bright future for the teenager, the lowest-ranked player in the draw at 570.
"He was able to win the first round against a tough opponent like (Dutch world number 73 Igor) Sijsling," Nadal said. "That's not the real ranking on him.
"He played two junior grand slam finals last year so he has a great future. He has the right level to try to be on the Tour very soon. Just keep working and that will happen."
As for his own game, Nadal said he played good first and third sets, and was particularly pleased with his serve.
"It was important that the serve was there during the whole match. It is very important here and it was working well."
Before the tournament began, Nadal said the court speed was much faster than when he was last here in 2012, having missed last year's Australian Open through injury.
The 27-year-old said the quicker surface made it tough for him to hit one of his best shots - the forehand down the line.
"Here that shot is a little bit more difficult because the court goes very quick when the ball bounces on the floor, so it's very difficult to adjust," he added.
"But I think I played at a very good level."