In Beijing's WTA 1000 event on Thursday, 19-year-old French Open champion Andreeva moved 2-0 up and fell 5-3 behind in a fluctuating opening set as both players struggled to hold serve, before recovering to edge the tiebreak.
Andreeva seemed firmly on course for a swift victory in the second, leading 4-1 and serving for the match at 5-3 before the 31-year-old Alexandrova staged a late fightback to force another tiebreak.
Andreeva took control of the breaker with a forehand winner for a 3-2 lead and won five of the final six points to seal victory and reach her first Beijing semi-final.
"What a match this was. I'm super happy with how it went. She played unbelievable today, and I'm very happy to get my very first win against her," said Andreeva.
Earlier, 26th seed Bartunkova reached her first WTA 1000 semi-final with a dominant 6-3 6-0 victory over fellow Czech, Wimbledon finalist Karolina Muchova, in 67 minutes.
The 20-year-old, who'd already stunned four-time grand slam champion Aryna Sabalenka in the last-32, controlled the contest from start to finish, winning five consecutive games to begin the match and the final seven games to complete the rout of one of the tour's top players.
"I follow her a lot," Bartunkova said of Muchova. "I have also similar style like her - playing lot of drop shots, volleys."
The win will take Bartunkova into the top-30 for the first time.
"For sure, I didn't expect it before this tournament," Bartunkova said. "I played lot of practice with top players - (Iga) Swiatek, (Coco) Gauff and others. Maybe it helps a little bit. It was one week before the tournament."
