Both players held their service games during the opening set, resulting in a tie-break. Stakhovsky twice lead with mini-breaks, but it was Djokovic who came out on top 7-5 to take the lead.
Russian Stakhovsky broke early in the next set to take a 2-1 lead. However, his advantage only lasted until the sixth game, when world number one Djokovic broke back before going on to wrap up the set and the match 7-6 6-3.
Djokovic will now take on his fellow countryman Janko Tipsarevic for a place in the final four of the competition.