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 yesterday.
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.
In front of a frantic crowd in the sold-out Belgrade Arena sitting 15,500 people, Djokovic relied on a solid serve throughout the rubber.
Djokovic showed some frustration before breaking Stepanek again for a 7-5 first-set win.
He then embarked on a spree to take the second set 6-1, before finishing Stepanek off in the third with a single break.
"I am happy with the way I played. Of course I was nervous at the beginning but it was very important for us to win the first set and then I relaxed," said Djokovic.
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," Stepanek said.
"I gave him quite a lot of trouble in sets one and three. I failed to earn a point (by winning the rubber), but it was great tennis," he added.
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