Haase rallied from a set down to beat fifth-seeded Feliciano Lopez, 4-6, 6-1, 6-4 in searing heat in the Swiss ski resort town.
The sixth-seeded Youzhny broke Victor Hanescu's serve twice in each set to beat the Romanian 6-3, 6-3. Hanescu, the 2008 Gstaad champion, was called for a time violation in the second set.
The 33rd-ranked Youzhny seeks his ninth career title on Sunday, and his third on outdoor clay.
The 57th-ranked Haase, who won his only two career titles on clay at Kitzbuehel, Austria, has an 0-4 career record against Youzhny.