The world number 12 will play the first-ever 500-level final of her career against either top seed Elena Rybakina or sixth seed Mirra Andreeva in Sunday's final.
Muchova, the 2023 Roland Garros runner-up, got the edge over Svitolina to claim the opening set as she converted two from two on break points against the Ukrainian.
The seventh seed's serve deserted her somewhat in the next frame as Svitolina hit back by breaking Muchova three times to claim the second set, which nonetheless lasted over 50 minutes.
The crucial moment in the decider came in the ninth game as Muchova pounced on Svitolina's service game to get her nose in front 5-4.
That sole break was enough as Muchova then served out the match to love, sealing the deal with an ace out wide.
Later, Australian Open champion Rybakina will look to continue her strong start to the clay-court season when she faces 18-year-old Andreeva, already a winner on the red dirt in Linz this year, in the other semi-final.
