The top seed reached the last four on Wednesday thanks to a tough win against the Croatian world number 29.
Djokovic had to come from behind to defeat Cilic, but he eventually fought back to seal his place in the next round.
"It was a tough five-setter. Coming in I knew Marin would play aggressively," the Serbian world number two told BBC Sport.
"He raised his game but I allowed him to come back into it. I was too passive on my strokes and he used his opportunities but I managed to find the right pace when I needed it."
Djokovic will now play Grigor Dimitrov for a spot in Sunday's final.