World number one Federer is looking to become only the third man in the Open era, after John McEnroe and Ivan Lendl, to win the title three years in succession.
Both players registered convincing victories to move into the second round of Wimbledon.
The world number one who won the Dubai Open on Saturday is hot favourite to complete a Gulf double at the Qatar Open.
The defending champion lost to Russia's Nadia Petrova 2-6, 3-6 in the quarterfinal.
The Czech announced her arrival on the world stage when she upset world number one Amelie Mauresmo at the French Open.
World number one Amelie Mauresmo denied nerves had caused her defeat in the fourth round
The top seed trailed 0-3 and 3-5 in the first set against Argentine qualifier Diego Hartfield before winning his first round match at the French Open.
Agassi and Mauresmo, both seeded fourth, hammered their way into the third round of the opening Grand Slam of the year.
Kim Clijsters recovered to beat Japanese qualifier Akiko Morigami 4-6, 6-1, 6-3 at the Italian Open
World number one Amelie Mauresmo won 4-6, 6-4, 6-4 to enter the semi-finals of the German Open.
Maria Sharapova will take on Slovakia's Daniela Hantuchova, while Amelie Mauresmo will meet Australian Alicia Molik in the semi-finals.
Andy Roddick ran out of firepower and was dumped by David Ferrer at the Nasdaq-100 Open.
Sania jumped 35 places to 99 in the latest world rankings.
Australian Open finalist Marcos Baghdatis lost to Nikolay Davydenko in the third round in Miami
The last time Martina Hingis appeared in the Fed Cup for Switzerland she was a 17-year-old four-times Grand Slam champion with the world at her feet.
Defending champion Patty Schnyder also reached the last eight by upsetting third seed Amelie Mauresmo 6-2, 6-2.
Nadia Petrova pulled off a stunning 6-3, 7-5 victory over the world number two and top seed.
The Swiss beat third seed Francesca Schiavone 6-1, 6-2 at the Qatar Open
Amelie Mauresmo saved a match point to beat Tatiana Golovin and set up a first all-French Paris Open final.
France's Tatiana Golovin also reached the last four of the Paris Open, claiming the scalp of third seed Nadia Petrova.
Sania Mirza lost to Tatiana Golovin 6-4, 6-2 in the second round at the Open Gaz de France
The third seed won her first Grand Slam title when the Belgian retired from the women's singles final because of injury.
The Indian ace and her American partner Corina Morariu will play 14th seeds Svetlana Kuznetsova of Russia and Amelie Mauresmo of France in the first round.
Amelie Mauresmo won the biggest title of her career on Sunday.
Jennifer Capriati and Elena Dementieva claimed semi-final spots at the U.S. Open after a day of drama, controversy and magical tennis.
The Frenchwoman advanced to the quarter-finals of the Advanta Tennis Championships with a 6-3, 6-4 win over Japan's Ai Sugiyama.
The French second seed was humbled by Slovenian qualifier Katarina Srebotnik at the Zurich Open.
Davenport saved two match points to beat Hantuchova and reach the quarter-finals of the Zurich Open.
Mary Pierce beat unseeded Italian Francesca Schiavone 6-4, 6-3 in the Kremlin Cup final to win her second title in Moscow
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