The Spanish star won 6-3 6-4 6-4 to book his place in the second round.
Nadal, currently ranked as the world number nine, was delighted to navigate his way past Mayer, who he feels is a difficult opponent.
He said: “I think I played solid match. I am happy the way I am playing. I had good weeks of practice.
“[It is] Never easy the first round. [There] Is always little bit more nerves at the beginning.
“I didn’t play against an easy opponent. The way that he plays is not a conventional game. You know, he changes a lot of the rhythm of the point, you know, changing with a slice, then he hit a winner.
“Then he play little bit slower ball. Is not easy to read his game, no? So just am happy the way that I played. I played good all the key points. That’s very important for me.”
Nadal is seeking to reach his first Grand Slam quarter final since the French Open 2014, with his last major success coming in the same tournament in the previous year.
The former world number one admits he is yet to rediscover his best form and is confident he can improve further.
He added: “Today I’m the ninth player of the world. I’m going to fight to not be worst, and I’m going to fight to be again better. I feel that if I am playing well and I am healthy, I think I can be much better.”
Nadal is 14/1 to win the Australian Open outright, Kei Nishikori can be backed at 25/1 and Milos Raonic is 16/1.
Later in the day defending champion Novak Djokovic took his place in round two with a 6-1 7-6 6-2 win over Fernando Verdasco.