The Olympic champion, who benefited from Jelena Dokic's retirement in the previous round while she was one set down, bowed out after two hours 12 minutes.
Stosur, seeded 30th, relied on a devastating forehand to break decisively in the eighth game of the first set.
Dementieva saved a set point as Stosur netted a routine volley but she was outwitted when the Australian came to the net after a weak service return.
Dementieva was the first to hold serve for 3-2 in the second set and she hung on to level the contest on her second set point when Stosur overcooked a forehand.
The Australian, who has only reached the fourth round of a Grand Slam once before, raced to a 4-0 lead in the decider and prevailed on her second match point with another forehand winner, to set up a clash with France's Virginie Razzano, who was a 7-5 7-5 winner over Italian Tathiana Garbin.
Russian Svetlana Kuznetsova's pursuit of a maiden French Open title gathered momentum when she dispatched Hungary's Melinda Czink 6-1 6-3 with the minimum of fuss.
The seventh seed was one of the in-form players coming into the championships and she ominously moved into the last 16 for the sixth year running. In three matches, Kuznetsova has lost only 11 games in total.
The first set disappeared in a blur for Czink, who surrendered it in only 22 minutes by whacking a Kuznetsova serve high into the stands.
The 26-year-old Czink offered some resistance in the second but it was never enough to trouble Kuznetsova who smashed the ball away on match point to seal a last-16 date with Polish 12th seed Agnieszka Radwanska, who had little trouble beating unseeded Ukrainian Kateryna Bondarenko 6-2 6-4.
Serbian fifth seed Jelena Jankovic stormed into the fourth round with a 6-1 6-1 crushing of Australian Jarmila Groth.
After luring her opponent into a false sense of security by dropping serve in the opening game, Jankovic quickly showed her who was boss by tearing through the rest of the se
Jankovic, chasing a maiden grand slam title, let her opponent have another consolation break in the sixth game of the second but her benevolence was short-lived and she claimed victory when 73rd-ranked Groth netted a forehand.
The former world number one, who has dropped just 10 games at these championships, will face Romanian teenager Sorana Cirstea, who beat Caroline Wozniacki 7-6 7-5 in the final match of the day after her Danish opponent had ben up 5-0 in the first set at one point.
Serena Williams overcame a sluggish start to beat Spain's Maria Jose Martinez Sanchez 4-6 6-3 6-4.
The American second seed will next face 24th seed Aleksandra Wozniak, after the Canadian battled to a 6-2 3-6 6-3 win over Spain's Lourdes Dominguez Lino.
Tennis | French Open Time Match schedule
10:00 Gonzalez F. v Hanescu V.
12:00 Murray A. v Cilic M.
14:00 Nadal R. v Soderling R.
16:00 Davydenko N. v Verdasco F.
10:00 Szavay A. v Cibulkova D.
12:00 Safina D. v Rezai A.
14:00 Azarenka V. v Ivanovic A.
16:00 Sharapova M. v Li N.
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