
The victory over the man who destroyed his Olympic dream four years ago at their first meeting in Athens was hard-fought, with Federer recovering from a break early in the second set after lifting the first.
Berdych, seeded 13th, nervously threw away two break points, the first on a missed drop shot and the second as he over hit a forehand.
That was all the opening Federer needed for a two-sets-to-love lead as he convert on his own first set point.
The Swiss, whose form had been somewhat tentative by his world-class standard, revved up in the third to sweep into the final eight against James Blake, a winner over Croatian Marin Cilic 6-3, 6-4, 6-4.
Federer's win in just under two hours was his 40th at the Open, where he is bidding for a third consecutive title and a 13th Grand Slam crown, which would bring him to within one of the all-time mark held by Pete Sampras.