The 26-year-old Baghdatis recovered from a set down to reach his fourth quarterfinal in 2012.
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The 21st seed came from one set down to beat the Serbian 1-6 7-5 6-3.
Jo-Wilfried Tsonga, seeded seventh, came from a set down to defeat Spain's Fernando Verdasco 4-6 6-3 6-2.
Italian second seed Francesca Schiavone came from a set down to beat Bulgarian Tsvetana Pironkova 3-6 6-3 6-1.
The world No. 36 came from one set down to beat Italian 21st seed Andreas Seppi 7-5 6-3 6-2 6-2.
In other matches, Feliciano Lopez battled back from a set down to defeat Xavier Malisse 4-6 7-6 (7-2) 6-4 in Paris.
In the women's draw, top seed Victoria Azarenka came from a set down to beat Belgian No. 28 Kirsten Flipkens 3-6 6-3 6-0.
Next up for Haas is third seed David Ferrer, who came from one set down to defeat Austria's Jurgen Melzer 4-6 6-3 6-0.
Next up for six-time grand slam champion Djokovic is France's Jo-Wilfried Tsonga, who came from one set down to beat Canadian Milos Raonic.
Djokovic will meet Nicolas Almagro in the final after the Spaniard came from a set down to defeat Janko Tipsarevic 2-6, 7-6, 6-2.
The Argentine won 6-3, 6-4, and will now face unseeded Bulgarian Grigor Dimitrov who came from a set down to beat Marcos Baghdatis.
Williams, who has battled injuries and illness, came from a set down to beat Chanelle Scheepers 4-6 6-2 6-3 in the opening rubber.
But rising French star Richard Gasquet progressed to the second round, coming from a set down to beat compatriot Arnaud Di Pasquale 3-6 6-3 6-4.
Novak will play Stefan Koubek in the last four after the Austrian fought back from a set down to beat Croatia's Ivan Ljubicic 2-6 7-5 7-5.
Once again he faced an uphill battle as Edberg recovered from a set down to lead two sets to one and was on top in the fourth.
The in-form Serbian had to come from a set down to beat Davydenko 3-6 6-4 7-5 in a late night encounter lasting over two and a half hours.
Safin, the runner-up in last year's final, came from a set down to win 4-6 6-4 6-2 and end Davydenko's bid for a fourth title in the Russian capital.
Meanwhile, on the women's WTA Tour, top seed Elena Dementieva of Russia fought back from a set down to beat Czech Lucie Safarov in the final of the Open GDF Suez tournament in Paris.
Serena powered to a 6-4 6-2 win over Australian Sam Stosur to book a meeting with Belarusian Victoria Azarenka, who recovered from a set down to beat Russia's Vera Zvonareva 4-6 6-4 6-0 in two hours and 28 minutes.
Williams, who next plays 26th seed Dominika Cibulkova after she came from a set down to beat Varvara Lepchenko, has never won the French Open and in 13 previous appearances, her best finish was a final place in 2002 when she lost to sister Serena.
And when the opening set came down to a tie-break unusually it was Hewitt who faltered, missing with two forehands as Safin pressed.
The CHC had previously told BBC Wales that negotiations with the health board were set to go "down to the wire".
Brannan, who is set to stand down as chairman has admitted to having invested several hundred thousand pounds in the Dens Park club.
Tragically just hours before Gibson was set to make the trip down to Wembley he suffered a stroke.
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Following the second of those, South Africa counter-attacked straight from the restart and Andries Bekker looked set to touch down in the corner, only for England prospect Noah Cato to bundle him into touch.
The care-home operator is set to shut down, after landlords owning all 752 of its care homes said they wanted to leave the group.
Now, after public concern over the locations, the trailers are set to be shut down, and the offenders moved to local shelters.
So Mitsubishi seems set to continue to be dragged down by the weight of history.
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