Berdych, who lost to Rafa Nadal in the 2010 final, came through 6-3 6-7(1) 6-3 3-6 6-3 in a two-hour-and-52 minute encounter on Court Three against the world number eight.
The Czech, who reached the quarter-finals for the fifth time, will next face either three-times champion Novak Djokovic or Adrian Mannarino.
Berdych, who had only won one of his previous 10 matches against top 10 opposition, was celebrating after firing down his 15th ace.
(Reporting by Toby Davis; Editing by Alison Williams)
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