The Swiss left-hander proved too consistent for the Russian, who struggled to hold her serve and was troubled by a blister on her toe, in a marathon match lasting almost three hours on Rod Laver Arena centre court.
The momentum clearly shifted in Schnyder's favour after she claimed the second-set tie-breaker 7-4.
Dementieva, runner-up at the French and U.S. Opens last year, gave Schnyder her third match point with a double fault and then lamely netted a volley.
Schnyder, who made the semi-finals last year in a career-best performance, will play either third-seeded Russian Anastasia Myskina or 19th seed Nathalie Dechy of France in the last eight.