Australia's Samantha Stosur returns in her first round match against Britain's Elena Baltacha at the French Open tennis tournament in Roland Garros stadium in Paris (Photo: AP)
The sixth-seeded Stosur, who won last year's U.S. Open title and reached the final at Roland Garros in 2010, beat Elena Baltacha of Britain 6-4, 6-0.
Kuznetsova won the French Open title in 2009 and U.S. Open in 2004 but is seeded No. 26 this year. Against Mirjana Lucic of Croatia, the Russian faced little trouble despite being broken once in the second set.
No. 20 Lucie Safarova of the Czech Republic also advanced, beating Anastasiya Yakimova of Belarus 6-2, 6-0.
Later, seven-time Grand Slam champion Venus Williams and 2008 French Open winner Ana Ivanovic were to play.
None of the top three men was in action in Paris on opening day, but former major champions Andy Roddick and Juan Martin del Potro were on the schedule.
Top-ranked Novak Djokovic and Roger Federer will be on court Monday, while Rafael Nadal is slated to begin his attempt for a record-breaking seventh French Open title on Tuesday.
Stosur converted five of her eight break points, and only briefly allowed Baltacha back into the match by being broken while serving for the first set at 5-3. The Australian broke right back to take the set.
In the second set, Baltacha won only four points on her serve, allowing Stosur to advance easily.
Kuznetsova raced through the first set of her match, and then held on to win the second to reach the next round. After trailing 3-0 in the second set, Lucic broke twice to get back to 3-3. Kuznetsova then won the next three games to take the match.
The 30-year-old Lucic reached the Wimbledon semifinals in 1999, but she is now 11-44 against players ranked in the top 30 in her career.
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