Joining Berdych on the sidelines were third seed Marin Cilic from Croatia who was beaten 6-6, 1-6, 7-5, by Frenchman and fifth seed Benoit Paire and fourth seed Stanislas Wawrinka, the 2011 winner from Switzerland, who crashed to a 2-6, 6-7 (6) defeat against another rookie face Aliaz Bedene Slovenia.
Surviving the mayhem was World No.9 and second seed Janko Tipserevic from Serbia who overcame Japan's Go Soeda 6-2, 6-4.
In the Saturday's semi-finals, Agut takes on Paire while Tipsarevic, last year's finalist, goes up against Bedene, the youngest player in the draw at 23 years, five months, and ranked a lowly 98.
The 24-year-old Agut, ranked 80 and playing a top-10 player for the first time in his career, showed a lot of courage and showcased his talent to stay with the 2011 semi-finalist Berdych, who never quite looked comfortable against an opponent who just went for his shots.
Berdych, not serving as well as expected, dropped the first set when Agut, one of the 13 Spaniards in top-100, broke him in the 12th, but the Czech star bounced back to take the second on three breaks of serve while himself dropping once.
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The stage was set for a humdinger of a final set that saw games going to serve until Agut broke Berdych in the ninth game to wrap up the match that lasted all of two hours and 17 minutes.
Earlier, surviving a mid-match slump, Paire took out twice champion Cilic to make it to the penultimate round, much against expectations in a match that swung from one end to the other.
Amazingly, the 23-year-old Paire, with a ranking of 47, survived as many as seven double faults besides 32 unforced errors, but conversely, fired 24 winners to Cilic's 22 and played the big points better to script a win that was not so much about how well the Frenchman played as how badly the Croatian, a first round loser here last year, did.
Cilic, winner here in 2009 and 2010, and ranked 15th, had his best moments in the second set when he seemed to get into the flow winning five games on the trot, and then led 2-0 in the third, but failed to drive home the advantage against an opponent who is among the most improved players on the tour.
The first set was rather flat with three breaks of serve, two of them by Paire in the third and seventh before wrapping up the set in 35 minutes. Cilic flickered briefly by breaking the Frenchman in the sixth, but otherwise was rather sluggish.
The match took a dramatic turn in the second set that Cilic took rather easily with breaks in the fourth and sixth games after surviving three breakpoints in the third even as the Frenchman made his frustrations known with high decibel screams.
The decider seem to bring the best out of Paire as he shrugged off a break of serve in the very first game and then fought his way back by breaking Cilic in the fourth and again in the 12th.
As the third set progressed, Paire played with a lot of freedom while Cilic became increasingly agitated as he erred in length and accuracy to play into the hands of the Frenchman.
The results (Prefix denotes seeding):
Singles (quarter-finals): Roberto Bautista Agut (ESP) bt 1-Tomas Berdych (CZE) 7-5, 2-6, 6-3; 2-Janko Tipsarevic (SRB) bt Go Soeda (JPN) 6-2, 6-4; 5-Benoit Paire (FRA) bt 3-Marin Cilic (CRO) 6-4, 1-6, 7-5; Alijaz Bedene (SLO) bt 4-Stanislas Wawrinka (SUI) 6-2, 7-6 (6).