At first glance, the 7-6 (7-1) 6-2 scoreline suggests it was a comfortable win, but it was hardly the case as the veteran Australian needed a little more than two hours to dispose of the Ukrainian.
Compatriot Maya Joint also progressed, beating Andorran Victoria Jimenez Kasintseva 6-3 6-2.
The 19-year-old Joint, currently sitting at a season-high ranking of 36, will next face Russia's Diana Shnaider, the world No.11.
Earlier on Thursday, Tomjlanovic, 32, who has been beset by injuries throughout her career, made a slow start and found herself 4-0 down in the opening set.
But the one-time world No.32 rallied to take it to a tiebreaker before conceding just one point to win the opening stanza.
It appeared to break the resolve of Starodubtseva, who won just two games after that to bow out.
Currently world No.94, Tomjlanovic had a mixed day with her serve, making eight double faults to go with five aces. Â
Tomjlanovic will have to raise her game if she wants to progress to the last 32 with fifth seed Jessica Pegula her next opponent.
In other results, there were straight-sets wins for Turkey's Zeynep Sonmez, Romanian Elena Gabriela Ruse and Anastasia Potapova of Russia.
Colombia's Camila Osorio and Aliaksandra Sasnovich from Belarus progressed in three.
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