The 29-year-old Serbian had won 23 of his previous 25 matches against Berdych and was never seriously threatened on his way to a 6-3, 7-5, 6-3 victory.

Berdych secured a break as the third set began but Djokovic immediately replied with one of his own before the match was suspended for 10 minutes due to rain at 3-3.

No sooner had play resumed, Djokovic broke to go 5-3 ahead before holding serve to wrap up victory.

The closest the world number one came to quarter-final elimination was through a potential disqualification in the third set.

He was relieved to receive just a code violation after letting his racquet slip out of his hand while angrily swiping at the ground, narrowly missing a line judge.

"I am aware that I have been lucky," Djokovic, the 11-time Grand Slam winner, said.

"It was just some unfortunate bounce, but fortunate ending of the scenario.

"That's all I can say."

Awaiting Djokovic in tomorrow's penultimate round is Austrian 13th seed Dominic Thiem, who reached his first Grand Slam semi-final by beating Belgian 12th seed David Goffin 4-6, 7-6, 6-4, 6-1.

The winner will meet either British number two seed Andy Murray or defending champion Stan Wawrinka of Switzerland in the final.

In the women’s draw, top seed Serena Williams moved a step closer to winning a 22nd Grand Slam title after coming from behind to beat Kazakhstan’s Yulia Putintseva 5-7, 6-4, 6-1.

"She's unbelievable," said Williams of her opponent.

"I didn't think I was going to win that but somehow I did."

The 34-year-old American, attempting to equal the Open era record Grand Slam haul of Germany’s Steffi Graf, will play unseeded Dutchwomen Kiki Bertens in the last four tomorrow.

Bertens saw off Swiss eighth seed Timea Bacsinszky 7-5, 6-2 in today’s other quarter-final tie.

The other women's semi-final sees Spanish fourth seed Garbine Muguruza face Australia's Sam Stosur.