The British No.2, who turns 19 next week, hit 11 aces and a succession of forehand winners in a 6-2, 6-3 win to set up a tie with Petra Kvitova.
"I'll go in with nothing to lose again," said Robson. "I seem to play pretty well when I do that. It's going to be tough, two lefties playing each other.
"I haven't played a lefty in a while, so I'm going to have to try as best I can."
In other ties, Serena Williams enjoyed a double bagel by beating Edina Gallovits-Hall 6-0, 6-0, despite the American injuring her right ankle during the match.
World No.1 Victoria Azarenka and Caroline Wozniacki also both progressed.