Kazakhstan's Rybakina will face either world number one Iga Swiatek (21) for a place in the final, who beat qualifier Sorana Cirstea (32) 6-2, 6-3.
Muchova smacked a backhand crosscourt winner to break serve in the first set for a 3-2 lead and, despite having played several gruelling three-set matches at the tournament and having her left thigh wrapped, looked fresh.
The hard-hitting Rybakina struck back when she converted her sixth break point opportunity of the set by pouncing on a weak approach shot from Muchova, who then could not get her volley over the net for 5-5.
In the tie-breaker momentum swung firmly in Rybakina's favour when she sent a blistering backhand winner down the line for 4-4 and the 76-minute first set ended on a Muchova double fault.
The unseeded Muchova, a former top 20 player now ranked 76th, played nearly flawless tennis in the second set to force the decider.
In the third, the 10th-seeded Rybakina went up an early break on another untimely double fault by Muchova and held at love to push the advantage to 3-1.
Muchova continued to battle, saving two match points on her serve in the ninth game.
But Rybakina did not miss her third opportunity to secure the win, crushing her sixth ace to end the two-hour, 45-minute contest on a sunny day at the WTA 1000 event in the Southern California desert.
"It was a really tough match today," said Rybakina, who became the first Kazakhstani woman to make it to the tournament's semis.
"I served much better in the third. I didn't start that well at the beginning of the match. I was a bit slower than usual and here the conditions are not that easy for me.
"But in the important moments I played well."
