The Czech third seed battled back to see off his Croatian opponent 3-6 6-4 6-1 in two hours one minute.
The win earned Berdych his sixth ATP crown and first since triumphing in Munich in May 2009.
A single break gave world number 10 Cilic the first set and he had chances in the second but could only take one of his three break opportunities.
Berdych, a runner-up at Wimbledon last year who ended a run of six semi-final defeats this year to make it to the final, made the most of his two break points to level.
And the Czech showed no mercy in the decider as Cilic's serve went to pieces, winning just 33% of points on his first serve.