Number one seeded Stosur overcame American qualifier Christina McHale 6-1 7-5 while Russian second seed Dementieva was made to work a little harder on her return from injury before edging out Japanese veteran Kimiko Date-Krumm 3-6 6-3 6-4.
Stosur, who is ranked a career high number five and top seeded in a WTA tournament for the first time, relied on her big serve and forehand to repel her 18-year-old opponent, who also served well but could not contend with the Australian's power.
"I thought I played quite well," Stosur told reporters.
"She's a good player and mixes in some spin. I got off to good start, but she stayed with me pretty well in the second."
Stosur will next face Yanina Wickmayer in Friday's quarter-finals after the Belgian seventh seed eased past Slovakian Dominica Cibulkova 6-1 6-4.
Stosur reached her first grand slam final at the French Open in June and credits her recent success to establishing a game plan and sticking to it.
"It's not like I have changed anything dramatically overnight," she said. "It's just a combination of everything that I have been doing over the past few years and now it's all coming together.
"Once you produce some good results, it instills more belief."
RUSTY DEMENTIEVA
Dementieva was playing her first match since retiring in her French Open semi-final against eventual champion Francesca Schiavone.
The 28-year-old Russian injured a calf muscle during the tournament and was forced to pull out of Wimbledon, missing a grand slam for the first time in 11 years.
She was clearly rusty in the first set against the savvy Date-Krumm but eventually found her range off the ground and was able to stretch her opponent out in rallies.
The 39-year-old Date-Krumm tried to claw her way back into the third set after going down 0-3 but Dementieva was too strong with her returns and closed out the contest with a forehand winner.
"It took me a while to get my rhythm but she was playing very fast and flat and I'm not used to this kind of style," said Dementieva, who will play the winner of the match between fifth seed Maria Sharapova and Belarussian Olga Govortsova.
"She's very quick, she knows how to use your speed against you and it's difficult to control the ball when someone is pushing you so hard."
Third seed Agnieszka Radwanska also advanced with a 7-6 6-2 victory over Ukrainian Olga Savchuk.
(Editing by John O'Brien)
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