Images from day 3
The 21-year-old, who has been battling injuries and off-court controversies, was rusty to start with as she wasted a couple of break points and committed 11 unforced errors in the opener.
But Tulyaganova's patchy form worked to Sania's advantage and the Indian wrested the first set after a 40-minute see-saw battle.
Sania then showed some fine form in the second set, cutting down on her unforced errors besides breaking Tulyaganova twice.
Sania also did well to hold her serve and did not give away a single break point, outplaying Tulyaganova in just 29 minutes to advance to the second round of the season's first Grand Slam.
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