The Czech, seeded seventh, won 6-2 6-0 7-6 (7-5) and will face Andy Murray or Nick Kyrgios in the last four.
Berdych, 29, began working with Murray?s former coach Dani Vallverdu at the end of 2014.
An 18th successive defeat by third seed Nadal would have set a new record for men?s tennis.
Nine years after his last victory against the 14-time Grand Slam champion, Berdych took full advantage of an opponent struggling desperately to find his game.
Nadal, 28, was playing only his 12th match since Wimbledon last summer, and his first against a top-10 opponent since he beat Novak Djokovic in the French Open final in June.
He insisted there had been no physical issues, saying it was ?just not my day?, but added: ?You cannot expect to win matches in quarter-finals of a Grand Slam helping the opponent to play well.
?That?s what I did the first two sets. From the beginning of the third, I played with more character.
?More the way that I have to play to be where I want to be, where I have been for the last lot of years.?
A wrist injury and appendicitis decimated the second half of 2014 for the Spaniard and the lack of big matches told in dramatic style on Tuesday.
He won just two games in the first hour of play, failing to register a single point behind his second serve and underpowered on his usually fearsome forehand.
Berdych was attacking Nadal?s serve at will and dominant on his own, apparently cruising to victory, but there was a spark of life from the 2009 champion.
Finally fired up, Nadal found some big serves to fend off three breaks points and then two match points in the third set as Berdych moved to within touching distance of a landmark win.
The Czech appeared certain to reach his second successive Melbourne semi-final when he raced 5-1 clear in the tie-break, but back came Nadal once again to heap on the pressure at 5-4 and 6-5.
Faced with a fourth match point on his own serve, Berdych faltered with his first attempt only to fire down his biggest second serve of the tournament, leaving Nadal helpless.
?Without being at my top level of tennis I was able to be here in the quarter-finals,? added Nadal.
?It?s not a bad result at all for me arriving here the way I arrived: only with one match [in 2015], only with five matches in seven months.?