But Rafael Nadal stayed on course for a seventh title in the Italian capital with a three-set triumph over Spanish compatriot David Ferrer.
Second seed Roger Federer also made the semi-finals by overcoming big-hitting Pole Jerzy Janowicz 6-4, 7-6 (7/2) to set up a clash with French upstart Benoit Paire
Berdych, who had beaten top-seeded Djokovic only once in their last 14 meetings, prevailed 2-6, 7-5, 6-4 to book himself an unlikely place in the semi-finals against Nadal and boost his chances ahead of the French Open which gets underway on May 26.
"I just lost a bit of concentration. I started playing more defensively. The match turned around, he gained confidence and I had a few unforced errors. At this level you have to take the opportunities when they come to you."
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Defending champion Nadal came through a tough quarter-final against Ferrer prevailing 6-4, 4-6, 6-2 in a 2hr 46min slug-fest.
It was Nadal's second win over Ferrer inside a fortnight after his quarter-final victory on his way to the Madrid Masters title last week.
"I had the same motivation as in any other match so there was no question about looking for motivation. Even if the record with him wasn't good, one day you have to break it. Every streak has to finish some time, and I'm happy that it was today," said Berdych.