World number one Mauresmo recovered from a set down to beat Russian Elena Vesnina 5-7, 6-3, 7-6 with a gritty performance to set up a clash with eight-seeded Czech Nicole Vaidisova.
Number four seed Dementieva battled past Israel's Shahar Peer 4-6, 7-6, 6-3 while fifth seed Petrova beat fellow Russian Elena Likhovtseva 6-3, 7-5 and unseeded Chakvetadze defeated last year's runner-up Francesca Schiavone of Italy 7-6, 6-4.
Dementieva now faces Swiss sixth seed Patty Schnyder, who overcame Czech qualifier Iveta Benesova 7-6, 1-6, 6-1, in the last eight. Petrova will meet another Russian, Vera Zvonareva, while Chakvetadze takes on second seed Maria Sharapova.
Vaidisova overcame Australia's Samantha Stosur 6-4, 6-1 to set up her quarter-final with Frenchwoman Mauresmo, who was made to work hard by Vesnina, ranked 56 in the world.
Dementieva was also on the back foot in the first set and had to save a match point in the second before winning the tiebreak and then taking the third set after the plucky Peer had received treatment on court for a back problem.
In the men's draw, Mauresmo's compatriot Fabrice Santoro, seeded seventh, had little trouble beating Russian Konstantin Kravchuk 6-1, 6-1 to reach the quarters.
However, sixth-seeded Frenchman Julien Benneteau lost 6-2, 2-6, 7-6 to Belarussian Max Mirnyi, who will play top seeded Russian Nikolay Davydenko in the last eight.
Local favourite Marat Safin came back from a set down to beat Italian Daniele Bracciali 3-6, 6-1, 6-4 in their second round match.
