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The 26-year-old Zvonareva, ranked third in the world, recovered from losing the first set to seal a 3-6, 6-4, 6-2 win over Pavlyuchenkova, 19, who was also part of the Russian team that whitewashed champions Italy 5-0 in Moscow last weekend.
Zvonareva admitted she was not surprised to have lost the opening set as she struggled to cope with her first appearance of the year on clay.
She increased her confidence as the two-hour match wore on, however, before blasting down three aces in the third set.
Zvonareva now faces Australia's Samantha Stosur or Slovakian Daniela Hantuchova in Thursday's quarterfinals.
"She's good, we'll be seeing more of her in the future," said Zvonareva of her teenage opponent, who is on the verge of breaking into the world's top 20.
"It was my first game on clay this season, so I just hung in there.
"Last week I was practising with her a lot, but it is totally different in a match situation. It was hard to go out and play her, but it's part of the job."
Zvonareva said she is looking forward to getting in some clay-court practice here ahead of next month's French Open.
"I have been injured for the last couple of clay-court seasons. I know I can play well on the surface, I just need to get some practice in," she said.
There were shocks as French eighth seed Marion Bartoli and Italy's third seed Francesca Schiavone both went out.
Bartoli suffered the biggest upset as she was beaten in straight sets 6-4, 6-2 by German wild-card Kristina Barrois in just 85 minutes.
The German belied her ranking of 79th in the world to blast four aces down at her French opponent, ranked 12th in the world, who hit four double faults.
Barrios will face Poland's Agnieszka Radwanska in Thursday's quarterfinals after she put out Schiavone with an impressive 6-1, 6-3 victory.
"This is a huge success, because I was the complete outsider," said Barrois. "I have nothing to lose again now (against Radwanska).
"My mother is very ill, things are getting increasingly difficult at home, but every victory helps of course. I am lucky I have a big family."
Results from the third day of the WTA Stuttgart tournament (x denotes seeding):
Second Round
Vera Zvonareva (RUS x2) bt Anastasia Pavlyuchenkova (RUS) 3-6, 6-4, 6-2
Kristina Barrois (GER) bt Marion Bartoli (FRA x8) 6-4, 6-2
Agnieszka Radwanska (POL) bt Francesca Schiavone (ITA x3) 6-1, 6-3
Samantha Stosur (AUS x5) bt Daniela Hantuchova (SVK) 6-4, 2-6, 6-4
Caroline Wozniacki (DEN x1) bt Zuzana Kucova (SVK) 6-1, 6-2
Sabine Lisicki (GER) bt Li Na (CHN x6) 6-4, 7-5
Andrea Petkovic (GER) bt Jelena Jankovic (SRB x7) 3-6, 6-1, 6-3
Julia Goerges (GER) bt Victoria Azarenka (BLR x4) 4-6, 0-0 retired
Other WTA results
Results from the Grand Prix de SAR La Princesse Lalla Meryem at the Royal Tennis Club de Fes (seedings in parentheses):
Singles
First round
Polona Hercog, Slovenia, def. Chanelle Scheepers, South Africa, 6-7 (6), 7-6 (1), 6-2.
Melanie Oudin, United States, def. Lourdes Dominguez Lino (3), Spain, 4-6, 6-1, 6-2. ^Second Round=
Greta Arn (4), Hungary, def. Kristyna Pliskova, Czech Republic, 6-4, 6-4.
Simona Halep (7), Romania, def. Alla Kudryavtseva, Russia, 6-2, 6-4.
Nadia Lalami, Morocco, def. Aravane Rezai (1), France, 2-6, 7-6 (5), 6-4.
Kirsten Flipkens, Belgium, def. Eleni Daniilidou, Greece, 6-4, 7-5.
