The seventh seed won 3-6 6-3 6-4 7-5 to extend his unbeaten streak against the world number 23 to nine matches in a contest dominated by serve.
Anderson, one the tallest on the tour at six-feet, eight-inches tall, dispatched 19 aces to 11 from Berdych in a high quality match and even took the opening set.
However, Berdych’s pedigree eventually shone through in a match that fully tested the 27-year-old.
“I’m really happy to have another win and go through,” Berdych said.
“I’m happy to extend the winning streak. In terms of my game, I think everything is going well, going smooth.
“I just dropped a set, which is actually good to face a bit of challenge, not only winning 3-0, which could be really tricky.
“Once you get a very tough opponent, then you need to face a tough situation.”
Having lost his last eight previous matches against Berdych, Anderson had the opportunity to take the match into a deciding set when he led 5-2 in the fourth.
However, Berdych rediscovered his serve, splattering aces against the backboard to win five games in a row to seal the hard-fought triumph.
The 2010 Wimbledon finalist will now face a tricky encounter against the 20-year-old Australian star Bernard Tomic after he stunned ninth seed Richard Gasquet to progress.
“He can really be a danger,” Berdych said of Tomic.
“His game is very different to the other guys. I think patience is definitely going to be the word to stick on.
“You know, go on by one again. This is a very tough and tricky opponent.”