The seventh seed won 3-6 6-3 6-4 7-5 to set up a last-16 clash against feisty Australian Bernard Tomic.
Berdych and Anderson had played each other eight times in the last 18 months, and five times this year, with the former Wimbledon finalist winning on every occasion.
The 27th-seeded Anderson stands 2.03 metres tall and possesses one of the best serves in the game, but he was cut down to size by the heavy-hitting Czech who overcame losing the first set to scrap his way into the lead.
It was far from comfortable for 2010 Wimbledon runner-up Berdych, however, as he came close to being extended into a fifth set having won his opening two rounds in three.
Anderson served for the fourth set leading 5-3, but could not close it out and Berdych, who needed some treatment on his back, finished him off three games later, wrapping up victory with a service winner on his second match point.
After losing in the first and fourth rounds in the two year's since his charge to the final, the heavy-hitting Czech looks in the mood for another long run.
"In terms of my game, I think everything's going well," Berdych said. "Just dropped a set, which is actually good to face a bit of a challenge, not only winning 3-0 which could be really tricky because then you need to face a tough situation against a tough opponent.
"This is good that I have a match like this also for building up some confidence again."
Wimbledon results on Saturday, the sixth day of the 2013 tournament (x denotes seeded player):Men's singles
3rd rd
Tommy Haas (GER x13) bt Feliciano Lopez (ESP) 4-6, 6-2, 7-5, 6-4
Bernard Tomic (AUS) bt Richard Gasquet (FRA x9) 7-6 (9/7), 5-7, 7-5, 7-6 (7/5)
Tomas Berdych (CZE x7) bt Kevin Anderson (RSA x27) 3-6, 6-3, 6-4, 7-5
Ivan Dodig (CRO) bt Igor Sijsling (NED) 6-0, 6-1, 1-0 - retired
Andreas Seppi (ITA x23) bt Kei Nishikori (JPN x12) 3-6, 6-2, 6-7 (4/7), 6-1, 6-4
Juan Martn Del Potro (ARG x8) bt Grega Zemlja (SLO) 7-5, 7-6 (7/3), 6-0
Lukasz Kubot (POL) bt Benot Paire (FRA x25) 6-1, 6-3, 6-4
Fernando Verdasco (ESP) bt Ernests Gulbis (LAT) 6-2, 6-4, 6-4
Kenny De Schepper (FRA) bt Juan Monaco (ARG x22) 6-4, 7-6 (10/8), 6-4
Mikhail Youzhny (RUS x20) bt Viktor Troicki (SRB) 6-3, 6-4, 7-5
Women's singles
3rd round
Sabine Lisicki (GER x23) bt Samantha Stosur (AUS x14) 4-6, 6-2, 6-1
Laura Robson (GBR) bt Marina Erakovic (NZL) 1-6, 7-5, 6-3
Kaia Kanepi (EST) bt Alison Riske (USA) 6-2, 6-3
Agnieszka Radwanska (POL x4) bt Madison Keys (USA) 7-5, 4-6, 6-3
Tsvetana Pironkova (BUL) bt Petra Martic (CRO) 6-1, 4-6, 6-2
Roberta Vinci (ITA x11) bt Dominika Cibulkova (SVK x18) 6-1, 6-4
Li Na (CHN x6) bt Klara Zakopalova (CZE x32) 4-6, 6-0, 8-6
Mnica Puig (PUR) bt Eva Birnerov (CZE) 4-6, 6-3, 6-4
Sloane Stephens (USA x17) bt Petra Cetkovsk (CZE) 7-6 (7/3), 0-6, 6-4
Petra Kvitova (CZE x8) bt Ekaterina Makarova (RUS x25) 6-3, 2-6, 6-3