World number 81 Moutet will face Andrey Rublev in the final after downing top seed Wawrinka 3-6, 7-5, 6-3.
The 34-year-old Wawrinka is still waiting for his 17th ATP tournament victory and first since winning in Geneva more than two-and-a-half years ago.
The three-time Grand Slam champion had cruised past Slovenia’s Aljaz Bedene 6-3, 6-4 in the last eight earlier on Friday.
Moutet, 20, reached his maiden top-level final despite falling a set behind, breaking in game 12 to take the second set before easing through the decider.
Second seed Rublev beat Serbia’s Miomir Kecmanovic 6-3, 6-1 in the first semi-final, having earlier cruised past Pierre-Hugues Herbert 6-4, 6-3 in the quarters.
Rublev, a former US Open quarter-finalist, is looking for a third ATP singles title.