The Russian, seeded 20th, won 6-2, 6-4 and faces Argentine Gisela Dulko in the third round on Friday.
Dulko progressed when 10th seed Victoria Azarenka of Belarus withdrew while trailing 1-5 in the opening set.
Sania's exit wasn't entirely unexpected as she had already exhausted herself playing as many as four matches in the week.
The 160th-ranked Indian had beaten beat Portugal's Michelle Larcher de Brito 6-3, 6-2 in the opening round on Monday.
Prior to that the Indian, owing to her poor ranking, had to secure three straight wins in qualifying round to make it to the main draw.
It was the first time since 2005 that Sania, once ranked as high as No. 27, played a qualifying event for a Grand Slam main draw.
Sania's best performance in a major came in this tournament in 2005 when she reached the fourth round.
The two had faced each other once before, on the grass courts of Birmingham in June 2008, with the Indian winning in three sets 7-6, 3-6, 6-2.
However, things changed dramatically thereafter with Sania's ranking plummetting and Pavlyuchenkova's rising. The Russian, currently in the best phase of her nascent career, has reached a career high rank of No. 22, attained last month
The 19-year-old former junior champion won her first two WTA Tour titles at Monterrey and Istanbul earlier this year.
Pavlyuchenkova raced through the first set, breaking Sania twice, before the latter could find a foothold in the match.
Sania finally managed to break the Russian's serve in the sixth game of the second set but the latter broke back in the very next game and held serve to make it 4-4.
Pavlyuchenkova broke Sania's serve for a second time in the set in the ninth game and then then held her own to seal a comfortable win.
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