Second seed Daniela Hantuchova was stretched by Ukraine's Alona Bondarenko before edging through 6-4 1-6 6-3.
Chakvetadze, who this week qualified for the season-ending WTA Championships which begin in Madrid on Nov. 6, looked flat and barely competed against an aggressive opponent who took full advantage of the freedom she was given.
"It was my worst match of the year," said Chakvetadze, who lost in just 39 minutes. "Everything happened really quickly and I was just slipping on court, I didn't run well. It was nothing.
"It's a little bit frightening because she is not a big hitter. She is just moving you around and changing the pace and the rhythm but I just missed everything I could."
Sixth-seeded Schnyder surrendered only three points on serve in the first set and three in the second, overpowering her hapless opponent, moving well and striking some excellent serves and returns.
"I hit the spots however I wanted and she had a tough day with me today," said Schnyder. "She could never find her game and had no idea how to beat me."
SLIM CHANCE
The Russian is now withdrawing from an event next week in Quebec in order to prepare for Madrid but her confidence is low.
"Now I'm already thinking if it's a good thing that I qualify for there because with this kind of game I don't know what I'm going to do there," Chakvetadze told reporters.
Hantuchova, who has a slim chance of taking one of the two qualifying places still available for Madrid, dominated the opening set against Bondarenko after breaking for 1-0 when her opponent hit a double fault.
Bondarenko rallied strongly and levelled the match by claiming the second set as Hantuchova gave away many points with alarming ease.
In the final set, the Slovak saved a break point with a lob at 3-3. When she was forced into a defensive lob in the next game and offered Bondarenko an inviting smash, her opponent blasted the ball long to give Hantuchova a break for 5-4.
"What got me through the third set was just my fighting spirit, trying to do my best on every point," said Hantuchova.
"Even though sometimes it was not going my way and some shots I was not happy with, I was not fighting against myself and I tried to use all the energy against her and move on after every point I missed."
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