Federer, who is seeking to equal Pete Sampras's record for Grand Slam titles, appeared listless from the beginning of his fourth round match with the Czech, before he found his form in the middle of the third set and never looked back.
The Swiss second seed had numerous opportunities to seal decisive games in each of the opening sets but the 20th-seeded Berdych managed to find a booming serve, blistering return or a winner to halt Federer's momentum.
However, after Berdych missed a smash while 3-4 down in the third, Federer seized the initiative and drastically raised his game to take the match in three hours, 29 minutes, setting up a quarter-final with Juan Martin Del Potro.
The Argentine put a slow start behind him to advance 5-7 6-4 6-4 6-2 at the expense of Croatia's Marin Cilic.
At 20, Del Potro becomes the youngest quarter-finalist since Richard Krajicek in 1992.
The Argentine retired in round two on his both previous visits here but has now reached two consecutive Grand Slam quarter-finals after last year's US Open.
American Andy Roddick also booked his place in the quarter-finals, beating Tommy Robredo 7-5 6-1 6-3 and extending his perfect record against the Spaniard to 10 matches.
The seventh seed, who has only conceded one set to Robredo in their 10 meetings, overwhelmed him again to wrap up a comprehensive victory in one hour and 47 minutes.
Roddick, 26, has made the semi-finals three times at Melbourne Park in his seven previous visits but has yet to make the final.
His quarter-final opponent on Tuesday will be defending champion Novak Djokovic of Serbia, who kept alive his Australian Open defence with a 6-1 7-6 6-7 6-2 fourth-round win over Marcos Baghdatis of Cyprus that stretched into the early hours of the Melbourne morning.
Djokovic, who seems to be steadily growing in confidence with each match of the tournament, raced through the opening set in 25 minutes then fought back from a break down to win the second in a tie-break.
Baghdatis, a finalist at Melbourne Park three years ago, won the third in another tie-break but twice failed to hold his own service games in the fourth set as Djokovic finally sealed victory at 2.26am local time.
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