The Serbian cruised to a 6-3 6-3 win, gaining a measure of revenge for his Wimbledon semi-final defeat to Berdych in the same city earlier this year.
The world number six has suffered from a poor form since that breakthrough victory, however, and produced another error-strewn display on Monday.
Djokovic got off to the best possible start as he secured a break of serve in the first game of the match.
He then had four more break-point opportunities in a marathon third game but Berdych edged it to get on the board.
