Tauson won convincingly 6-3, 6-4, showing a better second serve. She finished the first set with an ace, and the match on a long serve return by the Russian.
Alexandrova was reached the third round of the Australian Open while Tauson, the 2019 Junior Australian Open champion, won a minor event in Germany off the main tour.
Tauson's only other win of note was in September against recent Australian Open finalist Jennifer Brady at the French Open.
No. 2 seeded Fiona Ferro barely avoided the same fate as Alexandrova, as she was made to fight for nearly three hours to overcome Magdalena Frech of Poland 5-7, 7-5, 7-5 in the empty hard court stadium.
Frech, ranked 161st, broke in the first game of the first set, but had to break Ferro again to prevent the tournament's leading Frenchwoman from serving out at 5-4. However, Ferro broke back and served out a second time.