The Czech overpowered the mercurial Italian from the back of the court, briefly allowing the Italian to work his way back into the contest in sets one and two as he struggled to land first serves, but the result was never in doubt after just over two hours in Margaret Court Arena.
Berdych will face Roger Federer in the last eight after the Swiss outmaneuvered Marton Fucsovics in a straight sets victory.
Fognini had been forced to go the distance against Julien Benneteau in the previous round and he was evidently carrying some rust in an opening set that raced away from him.
Berdych broke for a 2-0 lead before the Italian was able to settle into his rhythm, an inopportune double fault gifting the Czech the advantage.
Fognini constructed break back opportunities in games three and five but Berdych kept his cool, driving an unerring backhand down the line to save a break point in the third game.
Instead, the Czech secured the double break and later the set in 34 minutes; Fognini overexerting on a backhand from midcourt.
Set two, and thus the match threatened to run away from Fognini when he was broken to love to open the second frame.
Berdych claimed eight of the first nine points but he was uncharacteristically careless when he was broken back for two-all. The Italian had received treatment on his foot at the end of the first set but he did not appear physically hampered by the ailment.
The crucial break, however, went in the direction of the 32-year-old and he moved within a set of the quarterfinals after 47 minutes.
Fognini became embroiled in a dispute with umpire James Keothavong after he was called for a couple of foot faults and the Italian’s concentration wavered as Berdych lurked with intent.
The Czech broke in set three but parity was restored in the sixth game before a lengthy seventh game which encapsulated the contest. Fognini coughed up break point on another foot fault but a stunning forehand pass brought up deuce.
That was when Berdych struck, constructing a perfect rally before seizing his opportunity to inch forward and strike with a volley.
The 32-year-old consolidated the break of serve, strengthening his hopes of claiming a maiden Grand Slam crown as he passed a stern test on Day 7 in Melbourne.