Seventh seed Berdych cruised to a two-set lead over a surprisingly listless Ferrer but spontaneously collapsed in the third set under pressure from the dogged Spaniard.
Ferrer appeared primed to drag the match into an epic struggle but lost focus at 2-2 in the fourth set to surrender serve with a string of unforced errors.
Berdych grimly held onto the advantage, surviving a breakpoint when serving for the match, to seal a semi-final with either triple defending champion Novak Djokovic or eighth seed Stanislas Wawrinka.
"It was extremely tough. And a physically really tough match with David, always," Berdych said in a courtside interview, wearing his distinctive blue and white striped shirt.
"After losing the third set, I really was not playing my best.
"After that I just tried to re-focus on my game again."
Berdych mowed through the first set in half an hour, breaking the off-colour third seed twice and sealing it with a crunching second serve that the Spaniard could only bash wide.
The pair struggled to hold serve in the second set and Berdych captured the decisive break at 4-4 with a fierce backhand down the line before serving out the set with an ace.
Ferrer galvanised himself for one last push and saved a string of break points to hold serve in a marathon game at 2-2.
Fired up, he lightly shoved a linesman out of the way of his box to dump his towel, then roared through the next four games as Berdych imploded in a hail of unforced errors.
The rangy Czech left the court between the third and fourth sets and emerged to survive a lengthy service game at 2-2.
Having dominated play, Ferrer surprised by losing focus in the next service game and slapped a forehand into the tramlines to concede a break.
Berdych grabbed his chance with both hands and though repeatedly taken to deuce on serve, the Czech saved a breakpoint with a blistering forehand winner and closed it out after just over three hours with a huge serve.
Baseline pounder Berdych has now made the semi-finals of all four grand slams.
"That was definitely the thing which was on my agenda," Berdych, a former Wimbledon finalist, said, also celebrating his first win on centre court in Rod Laver Arena.
"The first thought I have right now, I just want to go rest and prepare myself because I'll definitively need it."