Djokovic, ranked No. 1 in the world, fell behind in the first set but rallied to carry off a 7-5, 6-3 victory over his Czech opponent, whom he has beaten in 11 consecutive meetings in his career.
Djokovic trailed 4-2 early in the set but broke Berdych's serve twice, including the final game in which Berdych double-faulted.
The second set remained on serve until the eighth game when Djokovic notched the only break of the set to take a 5-3 lead.
The win was the first at Dubai for Djokovic since 2011 when he won the tournament for the third straight year.