Djokovic, the world number two and recently-crowned ATP World Tour Finals champion, first beat 44th-ranked veteran Radek Stepanek, 7-5, 6-1, 6-4, in two hours and 10 minutes.
Seventh-ranked Berdych then put the Czechs level with a three-set win over 117th-ranked Dusan Lajovic — 6-3, 6-4, 6-3 in an hour and 54 minutes.
"I am happy with the way I played,” said Djokovic. “Of course I was nervous at the beginning but it was very important for us to win the first set and then I relaxed.
"I served well in the important moments."
Stepanek said he would have been happier had he won the rubber, before praising Djokovic's defence.
"I tried to dictate the pace, get him into difficult situations, but he got out of them," said Stepanek.
In the second rubber, the 23-year-old Lajovic offered some resistance, but the 28-year-old Berdych controlled the clash, earning a break in each set.
"It was a tough one,” said Berdych. “It was the first time I've seen him on court.”
Meanwhile, Lajovic described the game as a useful lesson.
"The biggest thing was that I wasn't holding my focus the whole match like he did and I think that is the biggest difference between me and top players," he said.
"Players like Tomas won't give you two chances if you don't take the first one."
Del Potro turns down Argentina over 'two-faced' approach
Juan Martin del Potro has declined to play in Argentina's Davis Cup tie against Italy next year and said efforts by the country's tennis association (AAT) to get him back on the team were ‘two-faced’.
"I won't be [available] in this first tie to be played against Italy," said Del Potro in a statement sent to AAT President Arturo Grimaldi and Davis Cup team captain Martin Jaite.
"I'm tired of being invited by email or messages and being pressured at the same time through certain media with stories about whether or not I'll play the Davis Cup, trying to make me look bad to public opinion. It seems to me a hypocritical two-faced stance.”
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