Delbonis battled to a 6-7, 6-4, 6-4 victory against Wawrinka in the quarterfinals, eliminating the biggest draw from the first ATP tournament held in the Swiss city since 1991.
The left-handed Argentine is ranked 74th in the world and plays with a two-handed backhand.
He managed to get the better of ninth-ranked Wawrinka who was bidding for his tenth ATP world tour title and third of this season, following wins in Rotterdam and Chennai.
The Lausanne native's exit is disappointment for tournament organizers who have also had to deal with unseasonably cold weather this week at the Parc des Eaux-Vives venue.
Delbonis is set to play sixth seed Joao Sousa, of Portugal, in a semifinal starting at 4pm on Friday.
Columbia's Santiago Giraldo, who beat second seed Marin Cilic in two sets in another upset performance on Thursday, is matched against Brazilian Thomaz Bellucci in the the other semifinal starting at noon.