Fighting to get the match back on serve, Potapova ultimately failed to convert four break points as Muchova frequently crashed the net en route to a one-set lead.
Potapova channeled her late momentum into a strong second-set performance, nabbing the lone break to tie the match up at one set apiece.
Though Muchova took a brief timeout between sets to address an injured thigh, she rediscovered her form from the first set in time to take a 5-3 lead, forcing Potapova back on defense.
The former champion made a brave last stand in the last game with more break-point chances, but Muchova saved three in total before ending the contest on her second match point.
Muchova, who lost a tough Australian Open second round to former world No. 1 Naomi Osaka, will next face either No. 4 seed Ekaterina Alexandrova or resurgent qualifier Petra Martic, a former world No. 14.
Earlier in the afternoon, Danish youngster Clara Tauson kept up her blistering start to the season with a straight-set victory over Anna Blinkova, setting up a hard-hitting semifinal with No. 5 seed Dayana Yastremska. A 2024 Australian Open semifinalist, Yastremska dropped a 6-0 second set on former world No. 3 Maria Sakkari to reach the final four.
