Second seed Kim Clijsters of Belgium thrashed French teenager Marion Bartoli 6-1 6-1 and now faces unseeded American Lisa Raymond, who toppled former French and Australian Open champion Mary Pierce 7-6 6-4.
Third seed Henin-Hardenne lost the first set and had to rally from a 4-2 deficit in the second to halt Dementieva's charge.
The Russian needed seven set points to win the first set, finally clinching it when Henin-Hardenne attempted an ill-timed drop shot.
"I was in trouble," Henin-Hardenne told reporters. "She was hitting very hard and putting me under a lot of pressure."
But Dementieva was a spent force after going 4-2 up in the second set and Henin-Hardenne took advantage by reeling off the next eight games.
"It was a very difficult moment (at 4-2 up)," Dementieva said. "I gave everything I had, I felt I couldn't move any more after that."
HEAT BREAK
After Henin-Hardenne took the second set when she forced the Russian into a forehand error, the players were given a 10-minute
"It was tough conditions and I was playing too far behind the baseline. I knew I had to change the way I played, I needed to go more inside the court so she was doing the running."
Sixth seed Chanda Rubin of the U.S. survived a stern test from ninth seed Jelena Dokic to win 1-6 6-3 6-4, while Russian Nadia Petrova overwhelmed seventh seed Daniela Hantuchova 6-1 6-3 to set up a quarter-final against Henin-Hardenne.
French Open semi-finalist Petrova was lethal, cracking 25 winners to only 11 from the slim Slovakian to follow up in style her victory over 12th seed Amanda Coetzer in the second round.
"I told myself before I got on court that because it was so hot and humid that I needed to play every point with all my strength and energy," said the unseeded Petrova, who banged seven aces. "I was very focused and kept the pressure on her."
Russian Elena Likhovtseva upset 10th seed Magdalena Maleeva of Bulgaria 6-4 6-3 while Russian teenager Svetlana Kuznetsova put out fellow countrywoman and 16th seed Elena Bovina 7-6 6-2.
Fourth seed Lindsay Davenport will play the night match against Russian Lina Krasnoroutskaya.
