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, you needed to have quick ideas and execute well today." The 19-time Grand Slam champion said of the Hungarian.
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.
The 32-year-old, who is on his way back from back problems, lost to the five-time Australian champion in the third round last year and the odds are heavily stacked again him.
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, i am going to get myself ready, it's all I can do, and prepare the best I can." Said the 19th seeded Czech.
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.
Relieved Rafa survives Schwartzman test
After crushing Maria Sharapova in the last round, she came up against gritty Taiwanese veteran Hsieh Su-wei who stunned the 21st seed by taking the first set on Rod Laver Arena.
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.
The win set Kerber up with a clash against American Keys, a semi-finalist in 2015 who has found a new lease of life under the guidance of former great Lindsay Davenport.
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."
Whoever wins that match will have a potential semi-final against world number one Simona Halep, although the Romanian first has to get past Japan's Naomi Osaka on Margaret Court Arena.
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. "He's playing great. He's fit. He doesn't have too many holes in his game," he said.
The winner will face either Austrian fifth seed Dominic Thiem or American surprise packet Tennys Sandgren.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ