Federer, who has barely played in the six months prior to the Grand Slam in Melbourne after an injury-hit 2016, was at his best at the Rod Laver Arena as he raced to a 6-2, 6-4, 6-4 victory in an hour and a half.
Three errors and two double-faults in the first two games capped a slightly shaky start for Federer, but the 17-time Grand Slam winner quickly settled and showed his quality with some exceptional movement and a variety of perfectly executed shots.
Indeed, along with his exquisite trademark backhand, the Swiss maestro showed off the extent of his considerable locker as he hit clean volleys and pinpoint down-the-line forehand winners.
Federer's first break swiftly followed, and a sliced backhand—courtesy of the net cord—sealed his second. It took him just 26 minutes to complete the first set.
The 35-year-old carried his momentum into the second set as Berdych struggled to contain him, and he broke the Czech in the opening game thanks to a wide forehand.
The remainder of the set followed serve, with Berdych unable to get near Federer despite the veteran landing only half of his first serves in—according to the Open's official website, the four-time winner in Melbourne won 11 of 12 points on his first and nine of 12 on his second.
As such, Federer was quickly within one set of the fourth round, and a sensational backhand put him a break up to open the third set.
It was all Berdych could do to keep pace with his opponent, but there was no closing him down—he wasn't able to take Federer to deuce once in the entire match—and the Swiss finished the tie off with a comfortable hold.
Per BBC Sport's Matt Davis, Federer was delighted with the match: "I always felt against better ranked players I will lift my game naturally and I know Tomas really well. You feed off each other, I didn't expect it to go this well, I knew it was a tough third round if I got there and I couldn't be happier right now."
He will meet fifth seed Kei Nishikori in the fourth round, but given how sharp he's playing and how fresh he'll be after racing through this match, he stands an excellent chance of progressing even further.
Indeed, he has won his last three meetings with the Japanese player—another performance like this and Federer may well make it four.