The world number one, who missed the tournament last year due to injury, saved three set points with the match at one set each, before going on to earn a 3-6 7-6 7-6 6-2 victory in three hours and 37 minutes at Rod Laver Arena.
"I was so lucky," said Nadal. "Especially on one set point, he missed an easy one. The fourth set was for me and I'm very happy for that. I love this tournament. I'm very happy to be in the semi-finals after missing it last year. I suffered a lot."