Once he raced through the tie-break, there only looked like being one victor and he wrapped up victory after two hours and 14 minutes, maintaining his record of not having dropped a set all tournament.
Federer started poorly and when Berdych jumped to a surprise 4-1 lead, the script was torn up.
Showing great mobility, the towering Czech neutralised the potentially tricky world number 25 in a sometimes tetchy two-hour contest on Melbourne's Margaret Court Arena on Monday.
And the tiebreak King eased through, handing just one point to a bemused Berdych who was wondering where it all went wrong.
"I had to get a bit lucky, a bit angry, a bit frustrated, a bit antsy", Federer said.
"Anyway, I have to stay calm because the match is not finished yet, so I'm just trying to stay calm until [I] finish the match".
He was shaking his arm during the first set and grimaced at times when serving using a remodelled action.
Kerber is on a 13-match winning streak while 17th-seeded Keys beat No 8 Caroline Garcia in the fourth round.
The young American player was absolutely ecstatic as he continued by saying, "This is my fifth Australian Open and I've lost in the quallies every year except this one - now I'm in the quarter-final."Before Sandgren reached his first quarter-final, Federer had made to the quarterfinals of Australian Open for the 14th time now".
During the first set, Roger looked visibly flustered following Berdych's quick 3-0 lead and though the Swiss star did battle back, it wasn't without incident.
The break seemed to deflate Berdych, and although he held a set-point in the 12th game, the set went to a tie-break.
Federer said he was looking forward to facing Chung. Then it was very hard with him again.
"I'm not going to walk away from this tournament and think it was awful because I had one bad match".
Federer was full of praise for Chung's "incredible" win over Djokovic, which the youngster backed up with a straight-sets victory over American upstart Tennys Sandgren.
It is the 11th time Federer has reached the final four of a Slam without dropping a set and, with Rafa Nadal out of action, he is clear favourite to win a 20th Grand Slam title and sixth Australian Open.
"First day after the (Davis) match was pretty okay", the top seed told reporters after a 6-3, 6-2 victory over unseeded Naomi Osaka of Japan in 81 minutes.
"I " m keen to play against him. When I played my best [in the past], I was able to beat him.