The world number one defeated the 27-year-old 1-6 7-5 6-4 6-7(5) 12-10 to set up a clash against Berdych for a place in the semi-finals of the Australian Open.
"I've been in these situations before," ESPN quotes Djokovic as saying.
"I remember last year when I won against [Andy] Murray in the semis after five hours, and then played against Rafa [Nadal] in almost six hours.
"I know I can recover. I know I have it in me. I'm not too much worried about the physical part. I was ready for it. I was ready to go the distance, and I've done so."
The match between Djokovic and Berdych will kick off at 8.30am UK time on Tuesday.