Second-ranked Djokovic won 6-4, 7-6 (5), 6-2 to improve his career record against Berdych to 15-2.
The best-of-five series will be decided in the final match Sunday between Radek Stepanek and Serbian Davis Cup rookie Dusan Lajovic.
Djokovic, who improved his winning streak to 24 matches since September, converted his first match point with an ace, bringing cheers from the boisterous Serbian crowd at Belgrade Arena.
The Czech Republic is defending the title. Serbia won its only Davis Cup title in 2010, beating France in Belgrade.