The 29-year-old Czech secured her fifth WTA 1000 semi-final berth in a hard-fought contest that lasted one hour and 47 minutes.
"It was very close, basically one point at the end. It can always change in tennis. I'm just very grateful I was able to win the last point," Muchova said.
The opening set was a tight affair, remaining on serve until 5-4 when Muchova found herself in trouble at 0-30 before reeling off four consecutive points to level at five games all.
She then capitalised on a shaky service game from World number nine Mboko to edge ahead, eventually converting on her third set point to take the opener.
The second set proved no easier, with both players holding serve all the way to a tiebreak. Muchova seized control with an early mini-break and kept her nerve to close out the match.
"She's an amazing player. Every time you play a top-10 player you go on the court and you don't know who's gonna win, who's gonna lose," she added. "I tried to stay focused and stay aggressive."
The win extends Muchova's excellent run, having now reached the fourth round or better at all five tournaments she has played in 2026, including beating Mboko to claim the Doha title in February.
She will face either American Coco Gauff or Switzerland's Belinda Bencic in Thursday's semi-final.