GALLERY: Top 10 WAGS of the Aus Open
Berdych, who was in the driving seat the entire match, powered his way to a 6-2, 6-2, 6-3 victory over Anderson in a match that lasted one hour and 58 minutes.
The pair have previously met on nine occasions during the last two years - including at the Australian Open in 2012 and 2013 - where Berdych came out on top in all nine matches.
Anderson got off to a great start in Melbourne, scraping through the first round, beating Czech Republic's 82nd-ranked Jiri Vesely 2-6, 6-7 (4/7), 6-4, 6-4, 6-4, in his opening match.
He then beat Austria's Dominic Thiem 6-4, 6-3, 6-4, securing his passage to the next round of the tournament.
In the third round, the big-serving South African put up a brave performance, beating Edouard Roger-Vasselin of France 3-6, 4-6, 6-3, 7-6 (7/5) 7-5.
Berdych will next face Spain’s David Ferrer in the quarter-finals.
Results from the Australian Open on Sunday (x denotes seeding):
Men's singles
Fourth round
David Ferrer (ESP x3) bt Florian Mayer (GER) 6-7 (5/7), 7-5, 6-2, 6-1
Novak Djokovic (SRB x2) bt Fabio Fognini (ITA x15) 6-3, 6-0, 6-2
Tomas Berdych (CZE x7) bt Kevin Anderson (RSA x19) 6-2, 6-2, 6-3
Stanislas Wawrinka (SUI x8) bt Tommy Robredo (ESP x17) 6-3, 7-6 (7/3), 7-6 (7/5)
Women's singles
Fourth round
Flavia Pennetta (ITA x28) bt Angelique Kerber (GER x9) 6-1, 4-6, 7-5
Li Na (CHN x4) bt Ekaterina Makarova (RUS x22) 6-2, 6-0
Ana Ivanovic (SRB x14) bt Serena Williams (USA x1) 4-6, 6-3, 6-3
Eugenie Bouchard (CAN) bt Casey Dellacqua (AUS) 6-7 (5/7), 6-2, 6-0