Federer had not dropped a set in his first four matches or even really broken sweat, but he was uncharacteristically flat as Berdych took a 3-0 lead in the first set.
The world No 2 produce his first sign of life when Berdych came to serve for the set, arguing with the umpire about a malfunctioning Hawkeye machine that made the correct call but would not display the graphic.
After a lengthy discussion, Federer returned to the baseline and evetually broke back, going on to force a tie-break which he dominated to win 7-1.
There was almost no looking back at that point for the No 2 seed, who started the match as an odds-on favourite for the tournament thanks to Rafael Nadal’s elimination yesterday.
Just over half an hour later, he was two sets to the good and Berdych was off the court receiving treatment on an apparent groin injury.
The Czech returned a little gingerly and was tested by an early Federer dropshot, and while he seemed to loosen up eventually, the match was beyond him.
Federer only allowed one more brief wobble, allowing some clean ball-striking from Berdych to earn a break back in the third before immediately regaining the advantage.
The Swiss appeared to be able to draw on reserves of energy and timing as and when he needed them. And with only now Hyeon Chung and either Marin Cilic or Kyle Edmund standing in his way, the level of form on show today may be enough to win him a 20th Grand Slam title on Sunday.
However, if he admitted he was struggling in the first set and had to gee himself up by arguing with umpire Fergus Murphy.
“I hung around, got a bit lucky, a bit angry, a bit frustrated maybe at the umpire,” Federer said.
“I actually thought the call was good anyway, probably taking the call away was right!
“I’m very happy I got out of that first set. I think it was the key to the match.”
Federer will play Hyeon Chung in the semi-finals on Friday (8.30am UK time).