Kazakh Rybakina laid down a marker by beating Melbourne Park champion Aryna Sabalenka in Sunday's Brisbane final but was well off the pace against world number 21 Alexandrova as she sought a second win in their fourth meeting.
The top seed found herself 4-0 down following an error-prone start before clawing her way back with some fierce ball-striking but the counter-punching Alexandrova held firm and broke again to clinch the opening set.
Rybakina, who meets Karolina Pliskova in her first clash at the January 14-28 Australian Open, fell behind even further in the next set and mounted another comeback before Alexandrova fought back from 0-40 down at 5-3 to clinch the win.
Up next for Alexandrova is former world number five Jelena Ostapenko, who continued to gain momentum for another tilt at a Grand Slam title with a 7-5, 6-3 win over Marta Kostyuk.
The 12th-ranked Latvian made her Grand Slam breakthrough by winning the 2017 French Open title and is starting to rediscover her top form for the Australian Open, where she will begin her campaign against local hope Kimberley Birrell.
"It was a tough match, but finally I won in two sets. I managed it," Ostapenko said.
"I feel I was striking the ball well. Even in the first set when it was 5-2 to 5-5, I still was playing my game and then at the end I found it. Just happy to be through."
Second seed Jessica Pegula overcame Anastasia Pavlyuchenkova 6-7, 7-5, 6-4 to set up a clash with Daria Kasatkina.
In the men's draw, Jack Draper stunned top seed Tommy Paul 6-1, 6-4 to book a semi-final against Alexander Bublik, who saved a match point to outlast Lorenzo Musetti 6-3, 6-7, 7-5.
Last year's Australian Open quarter-finalist Sebastian Korda advanced with a 6-4, 6-4 victory over local favourite Christopher O'Connell and meets Jiri Lehecka after the Czech toppled second seed Nicolas Jarry 6-4, 7-5.
At the Auckland Classic, top seed Ben Shelton made his third tour-level semi-final with a 6-4, 6-3 win over Roberto Carballes Baena and will play Taro Daniel next. Daniel dug deep for a 6-4, 6-7, 6-3 win over Alexandre Muller.
A wrist issue forced second-seeded Briton Cameron Norrie out of his contest with Alejandro Tabilo, who faces Arthur Fils on Friday for a spot in the final. Frenchman Fils won the first set against Daniel Altmaier and was up 1-0 in the next when his opponent retired with injury.
Elsewhere, top seed Elise Mertens reached the Hobart semi-finals with a 7-5, 6-0 win over Arantxa Rus and will face Daria Saville after the Australian rallied past Zhu Lin 3-6, 6-1, 6-4.
Second seed Emma Navarro reached her second semi-final in as many weeks by getting past Viktoriya Tomova and plays Yuan Yue following the Chinese player's 7-5, 7-6 win over Yulia Putintseva.
