The top seed had to come from behind to defeat the world number 26, but he was able to do so with three hours and 24 minutes on the clock.
Djokovic started the match dominantly as two breaks of serve saw him blitz his opponent 6-1 in what looked to be an ominous sign of things to come.
However, Cilic fought back in the second with a single break allowing him to level the contest 6-3.
Cilic failed to put away another six break points in the third as he struggled to break Djokovic's defence before the set was decided by a tie-break.
Both players struggled to hold serve in the breaker, but it was Cilic who eventually came through 7-4 to put himself in control.
Revitalised in the fourth, Djokovic triumphed 6-2 thanks to some trademark attritional tennis from the back of the court, and from there he failed to look back as two breaks allowed him to seal the gruelling victory 6-1 3-6 6-7(4) 6-2 6-2.