The 18-year-old, who beat Kim Clijsters in the last round, saw off the former French Open champion in three sets to become the first British woman to seal a place in the last 16 of a Grand Slam since 1998.
"I honestly don't know how I pulled that out," she said after the match. "I was bitterly disappointed after losing the second set after coming so close.
"I knew that if I just kept sticking with her and going for my shots that it could pay off, and it did."
Robson will now face defending champion Samantha Stosur for a spot in the quarter-finals.