Djokovic, who has now reached 13 consecutive Grand slam semifinals, avenged his 2010 defeat by Berdych -- a contest which propelled the Czech into the final on that occasion.
The 26-year-old was 3-0 down in the second set but wrestled back control of the match before seeing off his disheartened opponent.
"It was a close match -- it could have gone either way," Djokovic told reporters.
"He was a double-break up in the second set. I don't know how I got out of that, but I was serving and returning well.
"I have a commitment to go far in this tournament. I am playing some of my best tennis on grass even though it's not my preferred surface,"
World No.6 Berdych revealed his disappointment after his performance tailed off following a promising opening set and a half.
He said: "I can play better than I played today. If you give him too much then it's a lot."
Meanwhile, del Potro overcame an injury to his left knee to ease past World No.4 David Ferrer 6-2 6-4 7-6.
The Argentine hit 42 winners and 12 aces after slipping on the Centre Court surface early on during the last eight clash.
Del Potro, who had not reached the semifinal of a grand slam since winning the U.S. Open four years ago, is the second Argentine to reach the last four following David Nalbandian in 2002.
"I was really close," del Potro told reporters after being asked how close he was from retiring.
"I felt a lot of pain at the beginning of the match. It was exactly the same as before.
"It's really, really painful. I twisted my knee once again, but the doctor gave me some magic pills so I could finish the match. I'm so glad to go through."
Ferrer had problems of his own, revealing he was struggling with an ankle injury.
"I wasn't able to warm-up properly but it was fine during the match," he told reporters.
"I don't think his injury affected him. He was more focused and aggressive, served really well and deserved to win."