The Serbian overcame the fifth seed in two hours and 31 minutes on Rod Laver Arena, just two days after being pushed hard by Stanislas Wawrinka, triumphing 1-6 7-5 6-4 6-7 12-10 in four hours 43 minutes.
Djokovic, who is defending champion in Melbourne, said that he used all of his powers of recovery to be ready in time to face the Czech number one.
"I felt good enough to go another five hours," said Djokovic. "People who don't know tennis, who have never been in those kinds of situations, would not truly understand what the player has to go through - not just when you prepare for a Grand Slam, but also during a Grand Slam.
"After five hours of a match, you need to really put a lot of time into recovery, different kind of recoveries.
"I understand that many people have many different views and opinions, and I respect that. But I'm doing everything that is legal, that is correct, that is natural that I can, possibly can in my power, and it's working well."
The 25-year-old will now face David Ferrer in the last four.