The defending champion swatted aside one-time training partner Marton Fucsovics 6-4, 7-6 (7/3), 6-2 to make the last eight for an incredible 14th time.
The Swiss maestro, 36, has made at least the last eight every year since 2004, bar a hiccup in 2015.
"He played very well," the 19-time Grand Slam champion said of the Hungarian. "You needed to have quick ideas and execute well today."
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.
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Of the 13 quarter-finals Federer has contested in Melbourne, he has won the lot.
"I have no choice to choose the opponent and may the better man win," said the 19th seeded Czech.
"I am going to get myself ready, it's all I can do, and prepare the best I can."
Germany's Kerber is the only Grand Slam champion left among the women, and she was given a big fright as she chases her second Melbourne Park crown after beating Serena Williams in 2016.
At one point Kerber was serving to stay in the match, but she bounced back to win 4-6, 7-5, 6-2.
"Credit to her, she played unbelievable. I was running everywhere," said Kerber, who had a poor 2017 after starting the year as world number one.
"I was just trying to focus on every point."
Hsieh, ranked 88, was always going to be a threat after knocking out world number three Garbine Muguruza and the dangerous Agnieszka Radwanska en route to the fourth round.
- Enjoying the job -
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Seeded 17, she flattened French eighth seed Caroline Garcia 6-3, 6-2 in just 68 impressive minutes.
"I feel like I'm playing just solid, consistent tennis," said Keys, a US Open finalist last year. "I think today was a good example of that. I think I served well. I think I returned well."
The 22-year-old added: "Right now I'm definitely really enjoying my job."
The final women's match sees sixth seed Karolina Pliskova take on fellow Czech Barbora Strycova, seeded 20.
Novak Djokovic is also in action in a night match as he looks to reach the last eight in Melbourne for a 10th time, with a tough test against talented Chung Hyeon.
The glasses-wearing South Korean, ranked 58, upset fourth seed Alexander Zverev in five sets in the round of 16 and Djokovic is wary.
The winner will face either Austrian fifth seed Dominic Thiem or American surprise packet Tennys Sandgren.
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