Djokovic pleased to get through toughest test.
Djokovic wasted four break points in the first set and was broken twice in the second, but he ultimately came through to record a deserved 7-6 (7/5) 6-4 6-3 win against the seventh seed.
The top seed, who is yet to drop a set in the tournament, will play Juan Martin Del Potro in the last four.
Djokovic admitted afterwards that he thought he could have lost the match.
The 2011 champion said: "It was a strong start for me yesterday.
"I had a few break points, a few chances to break in the first set, but I didn't manage to do that and the tie break was decided by one mistake with a forehand at 6-5. "It was a very close match, it could have gone either way. 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."
Djokovic was glad to see fellow Serb and Manchester United captain Nemanja Vidic in the crowd, along with former Chelsea striker Andriy Shevchenko, who had also come to watch.
"It really means a lot to see Nemanja with Andriy here," Djokovic said.
"I have only met (Vidic) once before briefly, but we are glad that he accepted the invitation to come."
Vidic, who snubbed a ticket in the Royal Box on Centre Court to come and watch his compatriot, saw Djokovic fly out of the blocks.
The world number one fired down two big returns to earn a pair of break points, but Berdych saw off the challenge with a couple of forehand winners.
Djokovic is used to overpowering his opponents from the back of the court, but yesterday he met his match in the big-hitting Berdych in the first set.
The Serb often had to station himself six feet behind the base line in order to deal with Berdych's big returns, which sent his opponent slipping and sliding across the court.
Djokovic spurned another break point in the seventh game when he returned long and he vented his frustration by yelling and striking the net with his racquet, but in the end Djokovic battle through to the semi-finals.