"She just had a good tournament in Linz where she made a semifinal, losing to Lindsay Davenport 6-1 6-1, so I tried to beat that score," said the top seed after the second round match.
Hingis's next opponent will be seventh seed Elena Dementieva. Russia's Olympic finalist overcame Italian Silvia Farina-Elia 2-6 6-4 6-4.
Second seed and defending champion Nathalie Tauziat of France also reached the last eight with a 6-3 7-5 win against Japan's Ai Sugiyama.
Olympic men's champion Yevgeny Kafelnikov achieved his first win since Sydney, fighting off a stiff challenge from fellow Russian Denis Golovanov before reaching the second round 7-6 6-4.
Kafelnikov, beaten by Britan's Greg Rusedski in the first round in Vienna two weeks ago, was forced into a first set tie-break, which he won 7-4 with a crisp cross-court backhand.
Kafelnikov raced 4-0 ahead in the second set before Golovanov, who also hails from the same Black Sea resort of Sochi, began a comeback to level at 4-4.
The former French and Australian Open champion needed all his experience to break his opponent in the next game when Golovanov's backhand sailed long on a break point.
Kafelnikov also had a scare in the same game when he slipped on the fast centre court, and complained to the referee.
"A piece of the court suddenly came loose and it was a miracle that I didn't twist my foot," he said. "Fortunately, they came and fixed the problem."
The problem did not seem to bother Kafelnikov as he won the following game to clinch victory in 80 minutes.
"We have trained together many times in the past, but this was our first competitive match, so it was only natural that I wasn't 100 percent," said Kafelnikov.
"But in the end, everything was ideal for me -- I won in two sets."
Twice Kremlin Cup winner Marc Rosset of Switzerland became the first men's quarter-finalist, beating Swede Magnus Gustafsson 6-3 6-4.
He was joined by Wimbledon semifinalist Vladimir Voltchkov of Belarus, a 7-5 4-6 6-4 winner over Australian Andrew Ilie.
Russian teenager Mikhail Youzhny, ranked 133 in the world, upset Fabrice Santoro of France 6-4 6-2.