The world number one required one set to guarantee the runners-up spot in the Stan Smith Group behind unbeaten section winner Roger Federer who earlier beat Kei Nishikori.
Djokovic will face Rafael Nadal in the last four on Saturday with six-times champion Federer up against either Stanislas Wawrinka or home favourite Andy Murray.
Djokovic, bidding for a fourth consecutive title at the year-ender which has been hosted at London's O2 Arena since 2009, was well beaten by Federer on Tuesday to end a three-year unbeaten sequence on indoor courts.
But he bounced back to take the opening set with a couple of service breaks and, although far from his best, the Serb did enough to finish the contest in straight sets.
Czech Berdych's only chance of qualifying for the semis was to beat Djokovic in straight sets, although with two wins in 22 matches against him it was always a tall order.
(Reporting by Martyn Herman; editin by Ken Ferris)
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