The Frenchman will face Tallon Griekspoor in Saturday's showdown after the Dutchman secured a 6-4, 6-4 win over Canadian second seed Felix Auger-Aliassime.
The unseeded Moutet, whose only previous appearance in an ATP final was in Doha in 2020, broke twice in the opening set and remained solid on serve to take it 6-4.
Moutet's court craft kept his American opponent off balance throughout, with his lefty angles and slice disrupting Michelsen's rhythm.
The second set was a tighter affair, with both players trading early breaks. Michelsen created five break points at 4-3, but 26-year-old Moutet saved them all in a gutsy hold.
The American edged ahead 6-5, but Moutet responded with a composed service game to force a tiebreak.
Moutet went ahead 4-3 in the breaker and never looked back, sealing the match on his first opportunity and will now be bidding to win his maiden ATP title.