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STUTTGART, Germany (Reuters) - French Open champion Francesca Schiavone suffered a major setback on Wednesday when she was beaten on her first outing on clay this season at the Stuttgart Grand Prix.

The world number four skipped Italy's Fed Cup showdown against Russia last weekend as she wanted to spend more time preparing for her Roland Garros defense but her decision failed to pay off as she was humbled 6-1 6-3 by Poland's Agnieszka Radwanska in the second round.

While Schiavone works out a way to rediscover her winning touch on red dirt, she might want to take a few tips from world number one Caroline Wozniacki, who thumped Slovakian qualifier Zuzana Kucova 6-1 6-2 to cruise into the quarter-finals.

Wozniacki, with one eye set on the French Open starting in May, was broken in the first game but raced through the next eight before clinching the second set 6-2.

She will have a tougher task in the next round where she will face either local favorite Andrea Petkovic or former world number one Jelena Jankovic who play later on Wednesday.

World number three Vera Zvonareva survived an early scare to beat fellow Russian Anastasia Pavlyuchenkova 3-6 6-4 6-2.

The 19-year-old opened up a 5-2 lead as Zvonareva struggled with the pace and depth of her opponent's groundstrokes. Pavlyuchenkova clinched the first set on her third opportunity with a another fierce crosscourt forehand.

Zvonareva, who along with Pavlyuchenkova beat Italy in the Fed Cup semi-finals over the weekend, battled back in the second and got her first break at just the right time to grab the second set.

She broke her opponent again early in the third set, whipping a powerful backhand down the line to gradually carve out a 4-1 lead and clinched the match on her first match point when Pavlyuchenkova fired a backhand wide.

Sixth seed Li Na of China had no such escape plan against German Sabine Lisicki who eased past the world number six with a comfortable 6-4 7-5 win, her smooth claycourt game back on track after an injury-plagued 2010.

Germany's Kristina Barrois, a wildcard entrant, joined Lisicki in the last eight with her own upset, beating eighth-seed Marion Bartoli of France 6-4 6-2. She will now meet Schiavone's conqueror Radwanska.

(Writing by Karolos Grohmann; Editing by Pritha Sarkar)