The 29-year-old Federer, winner of a men’s record 16 Grand Slam singles titles and the third seed at Roland Garros in Paris, beat the 22-year-old Teixeira 6-3, 6-0, 6-2.
The Swiss lost serve just once in the match and had to use his second serve only four times as he shut out Teixeira in the second set.
“I was happy the way I played at the beginning,” Federer told reporters. “As I said the other day, I think the first set was important for me to see what the match would look like, and then during the second and third sets it was easier.”
Federer has dropped behind Rafael Nadal of Spain and Djokovic of Serbia in the ATP World Tour rankings since winning his lone title in Paris two years ago. Last year, his record run of 23 consecutive Grand Slam semifinals ended when he lost to Sweden’s Robin Soderling in the quarterfinals.
Second-seeded Djokovic was leading Victor Hanescu 6-4, 6-1, 2-3 when the Romanian pulled out. The victory sets up a meeting with Argentina’s Juan Martin del Potro, and extends Djokovic’s winning streak to 39 matches from the start of the year. No. 25 seed Del Potro got past Slovenia’s Blaz Kavcic in straight sets.
Seventh seed David Ferrer of Spain beat France’s Julien Benneteau 6-3, 6-4, 6-2, and Janko Tipsarevic, the 29th seed from Serbia, defeated Pere Riba of Spain 6-1, 6-3, 6-0.
Sergiy Stakhovsky of Ukraine defeated Kei Nishikori of Japan. No. 9 seed Gael Monfils of France also won, as did Steve Darcis of Belgium.
Top-seeded Caroline Wozniacki beat Aleksandra Wozniak of Canada 6-3, 7-6 (8-6) to reach the third round. The 20-year-old Dane is attempting to win her first Grand Slam championship.
She will keep the top ranking on the WTA tour if she makes the quarterfinals in Paris. Kim Clijsters could pass Wozniacki only if the Belgian wins the title at Roland Garros and Wozniacki is beaten in the early rounds.
“I started off really well, and everything was going the way I wanted it to,” Wozniacki told reporters. In the “second set she played better. I started to play a little bit worse. Thankfully I finished it in two sets. It could easily have been three.”
Last year’s runner-up, Samantha Stosur of Australia, defeated Romania’s Simona Halep 6-0, 6-2, and Julia Goerges, the 17th seed from Germany, beat Lucie Safarova of the Czech Republic 2-6, 7-5, 6-2. Svetlana Kuznetsova, the 13th seed from Russia, got past Romania’s Irina-Camelia Begu, while 10th seed Jelena Jankovic of Serbia beat Vera Dushevina of Russia.
Bethanie Mattek-Sands, the highest-ranked U.S. woman in the tournament at No. 34, beat another American, Varvara Lepchenko, 6-3, 2-6, 6-3. No. 14 seed Anastasia Pavlyuchenkova of Russia and Canada’s Rebecca Marino also reached the third round.
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