Berdych matched the world number one for large periods of the match and was two breaks up at one point in the second set.
However, Djokovic came back to secure a 7-6 6-4 6-3 win to reach the semi-finals, although he believes that Berdych could just have easily emerged victorious.
"It was a very close match, it could have gone either way," Djokovic told reporters.
"He could have won the first two sets, he had a double break in the second. I don't know how I managed to go ahead, I don't know how I turned it around. I am really happy with the performance. I am playing some of the best tennis on grass of my career.
"Tomas is a very powerful player. As you could see, we went toe to toe in the first set. It was a huge confidence boost to come back and go two sets up."
Djokovic's win sees him progress to the semi-finals, where he will face Juan Martin del Potro.