Former World No1 Novak Djokovic lost to Chung Hyeong in straight sets in the fourth round.
The match, which lasted over two hours, saw the Indo-French pair convert one out of two break points, while their opponents converted three out of 12 break points.
Second seed Federer will now play fellow veteran Berdych, a semi-finalist in 2014 and 2015 at his most successful major, who demolished Italy's Fabio Fognini 6-1, 6-4, 6-4.
Dimitrov downed the 17th seeded Kyrgios 7-6 (7/3), 7-6 (7/4), 4-6, 7-6 (7/4) in 3 hour 26 minutes and will face Britain's Kyle Edmund in the quarter-finals.
Nadal was taken to four tough sets in almost four hours before winning 6-3, 6-7 (4/7), 6-3, 6-3.
The unseeded Indians were beaten 1-6 2-6 by their 11th seeded opponents in a contest that lasted one hour and nine minutes at the Melbourne Park.
The Swiss great and wife Mirka had identical twins Myla Rose and Charlene Riva in 2009 and another set came along five years later, Leo and Lenny.
The assured Dane, a semi-finalist in 2011 who has never quite lived up to the hype in the majors, annihilated 19th-seeded Magdalena Rybarikova 6-3, 6-0 on Rod Laver Arena in her most impressive performance to date.
Roger Federer and Novak Djokovic kept up their relentless march towards a semi-final meeting at the Australian Open Saturday
Maria Sharapova was sent crashing out of the Australian Open in a crushing defeat by Angelique Kerber Saturday as Simona Halep survived a titanic struggle to make the last 16.
Veteran Leander Paes and Purav Raja fought off a match point to shock formidable fifth seeds Bruno Soares and Jamie Murray and progress to the men's doubles third round at the Australian Open on Saturday.
With the temperatures a manageable 26 Celsius (79 Farenheit) at Melbourne Park after two days of oven-like conditions, the Romanian looked out for the count against American Lauren Davis.
Rafael Nadal stormed into the round of 16 at the Australian Open Friday with a vintage performance as Grigor Dimitrov and Caroline Wozniacki kept their Grand Slam hopes alive on a hot draining day.
The 10th seeded Indo-French combination of Bopanna and Edouard Roger-Vasselin beat off a late fightback from Portugal's Joao Sousa and Leonardo Mayer of Argentina 6-2, 7-6 (7-3).
The 19-time major winner says the current agreement is a good one, but it has run its course and time was right for players to get together and seek pay increases.
Swiss 19-time Grand Slam champion Federer disposed of Jan-Lennard Struff 6-4, 6-4, 7-6 (7/4), avoiding the worse of the furnace-like conditions in his night match.
The three-time Grand Slam winner, who defeated Rafael Nadal to win the 2014 Australian Open, has slipped to nine in the world rankings and faces a battle to climb higher after his early round exit.
Djokovic said there was little indication that players were going to have any form of discussion with the sport's chiefs for a shorter season.