The Swiss star punished Clijsters for her 11 double faults in the two-hour match and imposed the first defeat on the Belgian since she won the US Open last month.
Second-seeded Clijsters struggled throughout with her service, landing only 58 percent of first serves.
Schnyder lost to Clijsters in the latter's first tournament in more than two years, at Cincinnati in August. But the tour veteran kept a cool head in the decisive tiebreak to beat Clijsters for the first time since 2005.
The defeat was only Clijsters' second in 26 main draw matches at Luxembourg, where she was seeking a sixth title.
Schnyder, the former top-10 player ranked 47th, will play Sabine Lisicki of Germany in the quarterfinals.
Another Belgian, Yanina Wickmayer, did better. She beat France's Alize Cornet 7-5, 7-6 (6) to earn a match against compatriot Kirsten Flipkens on Friday.
Earlier on Thursday, No. 4-seeded Daniela Hantuchova won a marathon second-round match against Czech Lucie Hradecka 7-5, 3-6, 6-2 to advance and will play her quarterfinal against Israel's Shahar Peer, who beat No. 8 Carla Suarez Navarro 3-6, 6-3, 6-1.
Hantuchova became the new tournament favourite. Top-seeded Caroline Wozniacki of Denmark withdrew in the opening round with a left leg injury and third-seeded Anabel Medina Garrigues lost in the second round.
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