Ukraine’s Stakhovsky carved out a 6-4, 3-6, 6-4 victory over the Swiss former Australian Open winner, and now meets Frenchman Gilles Simon.
World number 17 Simon shrugged off a slow start to subdue compatriot Jeremy Chardy 7-5, 7-6 (8/6) and set up a last-four match-up against Stakhovsky.
In the second semi-final, seventh seed and home favourite Gael Monfils will play Spaniard Roberto Bautista, the fourth seed, for a place in Sunday’s championship match.