It wasn't easy early as Berdych grabbed an early break for 3-0 but he couldn't serve it out.
A dismayed Berdych didn't mount much of a test after that.
After Federer applaud his opponent saying, "I was just frustrated and a bit antsy".
"That's why I was under pressure. It ended up being the key of the match", Federer said on court after his win. "May be because I stole the first set from him, he felt dejected", Federer joked. Got off to a good start there.
It was different a year ago, when Federer was coming back from a long break and played a series of lengthy matches.
"It was not my best start", said Halep. "So I'm feeling good".
Federer said he has been impressed with the way the two unseeded players have progressed, particularly Chung's run. One thing I know is I'm going to be playing aggressive. If she wins the title, she will make history with no woman ever crowned champion in a maiden Australian tournament.
"I (have) never played in the second week in a grand slam, so I'm really surprised".
He added: "I make the semis, I beat the likes of Sascha, Novak, and other good players".
Both players had produced their own fairy tales at the season's first Grand Slam event before their showdown.
He is also projected to crack the top 30 in the upcoming Association of Tennis Professionals rankings.
Federer is the tournament favourite and will be vying for a monumental twentieth Grand Slam title, after Rafael Nadal retired against Cilic in the quarter-finals.
Day 10 of the Australian Open saw the enduring class of Rodger Federer get the better of Tomas Berdych, whilst young pretender Hyeon Chung will meet the Swiss superstar in the semi-final after defeating Tennys Sandgren.
The Romanian will now play Kerber on Friday, with the victor to face the winner of Thursday's tussle between world number two Caroline Wozniacki and emerging star Elise Mertens.
"After the deuce break point, no ceremony, just keep focused".
But after seeing Chung dismantle an admittedly battling Novak Djokovic, Federer isn't taking the youngster's skills for granted.
Advised that the call had gone against him and he had lost his last remaining challenge, Federer admonished chair umpire Fergus Murphy in a rare display of annoyance from the ice-cool veteran.
"He's incredibly impressive in his movement, he reminds me a lot of Novak the way he is able to slide forehand and backhand and use the hardcourt as a claycourt".
To beat (Novak Djokovic) here is one of the tough things to do in our sport.