But there was no such luck for Spanish third seed Arantxa Sanchez-Vicario, who was beaten 6-3 6-2 in 58 minutes by Bulgarian Magdalena Maleeva in a second round match.
Fourth seeded Anna Kournikova advanced by eliminating fellow Russian Vera Zvonareva 7-6 6-4, while fifth seed Amelie Mauresmo also made the last eight, beating American Lisa Raymond 6-2 6-4.
In the men's tournament, U.S. Open champion and top seed Marat Safin of Russia hit 15 aces on his way to a 6-1 7-5 win over Italian veteran Gianluca Pozzi.
"Pozzi is 35 years old, he is almost from a different era, but he has a very good feel for the ball and can hit some tricky shots," said Safin, who faces Wimbledon semifinalist Vladimir Voltchkov on Friday.
"It will be a totally different game against Voltchkov. We've played a lot in our youth and until now I've never beaten him, never even came close, so now I'll be gunning for revange," Safin said.
Second seed and defending champion Yevgeny Kafelnikov of Russia had little trouble against Spaniard Alberto Martin, winning 6-3 6-1.
The Sydney gold medalist now takes on German qualifier Lars Burgsmuller, who upset eighth seeded Czech Jiri Novak 5-7 6-1 6-3. Sixth seeded Max Mirnyi of Belarus also lost to Swede Jonas Bjorkman 6-3 3-6 6-1.
But the day belonged to the women's tournament as Hingis, who had dropped only one game in her second round match on Wednesday, continued her roll against Dementieva -- winning the first set in just 14 minutes and taking a 2-0 lead in the second.
ALL TOO EASY FOR HINGIS
Then, suddenly the match turned upside down as Dementieva took the next four games.
"It was going very well for me, almost too easy," Hingis said. "And I probably lost my concentration a little bit. I also changed my racquet at 2-1 and suddenly I couldn't hit my serve."
The world number one came back to level the second set at 6-6, but the Russian seventh seed kept her cool in a tie-breaker to win 7-5 and force a decisive third set.
It was evenly balanced until the ninth game, when two errors and a winner from Dementieva left Hingis facing three break points on her serve. But she held on to take a 5-4 lead.
Then it was Dementieva's turn to erase two match-points against her with two forehand winners for 5-5.
CLOSE TO DEFEAT
But the Russian's serve let her down in the 12th game when she hit two double-faults in a row, enabling Hingis to clinch the match after nearly two hours.
"I was close to losing this match when I was 0-40 down on my serve in the ninth game of the final set," said Hingis. "It was a very important game, but still I'm not totally happy with my performance tonight. It was too many ups and downs in my game."
Dementieva said she was just too timid near the end of the match.
"At 4-4, I had three break points, but instead of attacking Hingis, I just waited for her to make mistakes," she said.