The current British number one dominated the encounter from the outset and went on to knock out the 10th seed with a 6-3 6-4 victory.
"What a first-class performance! She hit the ball so cleanly with so many winners, Kirilenko didn't really have a look-in. It was really stunning, I don't know if she can keep up that sort of quality because it was out of this world," Wade told BBC Sport.
Robson has never gone beyond the second round at SW19.