The unseeded Czech fought back from 5-2 down in the deciding set to claim a 7-6 (5) 6-7 (5) 7-5 victory in a tremendous contest lasting three hours and 13 minutes.
It was a stunning performance from Muchova but also a stunning collapse from Australian Open champion Sabalenka who, having held match point, won just four of the next 24 points.
“I got on the better wave,” said the world number 43. “I could see that she was struggling a little bit and doing fast mistakes. I was just trying to keep her there.”
The expected battle between the world’s top two players did not materialise but Swiatek kept up her end of the bargain with a 6-2 7-6 (7) victory over Beatriz Haddad Maia and will be a strong favourite to win a third Roland Garros crown and fourth slam overall.
If Muchova can produce the same all-court wiles she showed against Sabalenka, though, she could yet become the latest surprise slam champion.
The 26-year-old was playing in her second slam semi-final having also reached the last four at the Australian Open in 2021, but injuries severely restricted her last year, with her ranking dropping outside the top 200.
Muchova said: “Some doctors told me, ‘Maybe you’ll not do sport anymore’. But I always kept it positive in my mind and tried to work and do all the exercises to be able to come back.
“I think everything has its own time. In the past, it was not easy. That’s actually what makes me appreciate this result even more now, because I know what I have been through in the past.
“To be now in a grand slam final, it’s for sure my dream. I’m super, super glad that I’m here and that I’m going to play finals on Saturday.”
Belarusian Sabalenka, who has found attention more on her off-court views than her tennis this fortnight, made the faster start but Muchova grew steadily into the match and made the first big move, breaking for 5-4.
Back came Sabalenka immediately, though, a forehand winner saving a set point and then more crunching groundstrokes earning her the break.
It was a compelling contest between the raw power and aggression of Sabalenka and the more subtle skills of Muchova, who gave a masterful display of using angles and changes of direction as well as being very willing to come to the net.
She is not averse to a winner, too, and produced one from the top drawer on her second set point at 6-5 in the tie-break, drilling a backhand down the line.
The old Sabalenka might have fallen away quickly in a barrage of errors after being broken at the start of the second set but she regrouped impressively, thumped groundstrokes with ever greater intensity, and levelled the match.
When pressure in the decider finally told on Muchova as Sabalenka broke for 4-2, it seemed the script was written, but the ending did not play out as the second seed had hoped.
Sabalenka was philosophical afterwards, saying: “She played unbelievable tennis. Still, I had a lot of opportunities, and I didn’t use it. Of course I’m very disappointed with this tough loss, but that’s OK.
“She kind of stepped in and started playing a little bit more aggressive, and I kind of lost my rhythm. I wasn’t there.
“What I was doing, and hopefully I will keep doing it this season, that’s incredible, just next level. I don’t look at this tournament as a negative tournament. I think I did a great improvement on the clay court, and it’s my best result here.”
Sabalenka was one of the Russian and Belarusian players sweating over receiving their visas for the UK but the 25-year-old revealed she now has the correct paperwork and will be able to play Wimbledon.
“I’m super excited,” said the former semi-finalist. “I really like to play there. I really enjoy the atmosphere. I really missed last year Wimbledon and I just can’t wait to come back and show my best tennis.”
The second semi-final was also a fine battle, with Haddad Maia, the first Brazilian woman in the open era to make the last four here, not wilting at all after her marathon efforts.
She had spent more than twice as long on court as Swiatek but the pair engaged in some terrific extended rallies, particularly in the second set, when Haddad Maia led 3-1 and had chances to extend her opponent to a third set for the first time this tournament.
The best of those came at 6-5 in the tie-break but Haddad Maia netted a tight forehand and, although she saved a first match point in spectacular fashion, Swiatek powered away a forehand on the second before punching the air.
The 22-year-old said: “It’s really amazing. I’m happy that I’m able to play consistently, every year have a good result here, so I’m pretty excited for Saturday.
“It wasn’t easy, she’s a fighter. I’m happy that I played so well in the tie-breaker. I’m just glad that I was solid and I managed to finish these last shots.”