Djokovic, who has ever won the French Open crown, will face 13th-seeded Dominic Thiem after the Austrian defeated 12th-seeded David Goffin of Belgium 4-6, 7-6 (7), 6-4, 6-1 in another quarterfinal match.
"I'm very pleased to be in semifinals of another Grand Slam," Djokovic said afterward. "But because of the fact that I have to play every day, my focus right away goes for recovery and the next match. I don't have much time."
On the women's side, top-seeded Serena Williams had to rally to dispatch of 60th-ranked Yulia Putintseva 5-7, 6-4, 6-1 to reach the semifinals.
Williams will face 58th-ranked Kiki Bertens of the Netherlands in the semis. Bertens stunned eighth-seeded Timea Bacsinszky 7-5, 6-2.
Williams was dangerously close to being unceremoniously ousted in straight sets by the unheralded 21-year-old Russian before staving off defeat and finishing with a strong third set.
"She played unbelievable. And I honestly didn't think I was going to win that in the second set," Williams told reporters. "Somehow I did."
Williams made 24 unforced errors in the opening set -- Putintseva made just two -- before eventually finding her form.
"I thought, I just can't go out in straight sets," Williams said. "So I just thought if I could just win a set. ... At that point, I wasn't playing my best, but she was just playing some different tennis and I just wasn't used to it.
"I had to get into that rhythm, and once I found it, I found my game."
Williams is seeking to win her 22nd Grand Slam title, which would match Steffi Graf's record.
Bertens has defeated four consecutive seeded players to reach the semifinals. She briefly needed medical attention for a left calf injury after the first set before going out and finishing off Bacsinszky.
Fourth-seeded Garbine Muguruza of Spain will face 21st-seeded Samantha Stosur in the other women's semifinal.
Djokovic's match was interrupted by rain with the third set even at 3-3 and that greatly disturbed Berdych. After play resumed, Djokovic sailed through the final three games to close the match.
"That was one of the worst calls that I ever had on the court," Berdych said. "We were playing 2 1/2 sets in the light rain."
Berdych felt the stoppage halted his momentum. He also was miffed over the explanation he received.
"When the referee came down and she told us 'We wait a few minutes, if it [the rain] stops or not,'" Berdych said. "I was like: 'Waiting for what? What's the point of this?' The court won't get better. It will get only get worse. We will be sitting in 10 degrees here, and there is no sense at all."
Thiem will be attempting to end Djokovic's title bid. This will mark Thiem's first semifinal in a major.
Second-seeded Andy Murray of Scotland faces third-seeded Stan Wawrinka of Switzerland in the other men's semifinal.