Sania, who had lost in the first round in Stanford and slipped to 35 in the rankings, beat world no.190 Hrdinova 6-3, 6-4 in an hour and seven minutes on Tuesday.
The Indian ace, seeded 16th, saved seven of the nine break-points to make the cut.
Sania admitted to still feeling some pain in her surgically repaired right wrist, but she was able to get her huge forehand working against the tall Hrdinova.
"It's getting better every time I go on the court," Mirza said.
"She had nothing to lose and has one of the biggest serves I've faced. I returned well and although my serve got a little shaky in the second set, it was great to get a win."
She will next face the winner of the match between Ukraine's Kateryna Bondarenko and Meng Yuan of China and could meet Serena Williams in the third round.
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