Federer, who needed four-and-a-half hours to see off Janko Tipsarevic on Saturday, looked much more at ease against the Czech, although he did have a few anxious moments in the second set before wrapping up the win in just under two hours.The Swiss star will face James Blake in the last eight after the American had earlier beaten Marin Cilic in straight sets.It was apparent early on that Berdych was not going to give Federer many opportunities to establish an advantage.
But the world number one was just as resilient, conceding just four points on his own serve in the first set before breaking Berdych late on to win it 6-4.
The Czech secured the first break of the second set but a determined Federer broke back quickly to level.
Both men looked strong on serve and it was no surprise when the set went to a tie-breaker.
Berdych twice made unforced errors on set-points and then made another to lose it 9-7 and go two sets down.
Federer upped his game in the third and was completely dominant on serve - and Berdych finally cracked in the sixth game when he was broken to love.
From that point on it was simply a matter of Federer serving out the match, and he did so with consummate ease.