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
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.
McEnroe wins doubles match on Stockholm return
Roddick recovers to defeat Gasquet in Vienna