Lisicki, who knocked out defending champion and top seed Serena Williams in the fourth round, broke Kanepi's serve in the opening game of the match on Court One and wrapped up the first set in 33 minutes.
Estonian Kanepi took advantage of three Lisicki double faults to break serve for a 2-1 lead in the second set but the German 23rd seed reeled off four games in a row to stand on the brink of the last four.
Kanepi held serve to stop the rot but Lisicki sealed victory in just 65 minutes with a forehand volley on her third match point.
Lisicki will play fourth seed Agnieszka Radwanska in the semi-final.
The Pole survived a tough challenge from sixth seed Li Na to win 7-6 (5), 4-6, 6-2.
The final game lasted for more than 10 minutes before Radwanska finally sealed it on her eighth match point.
Image: Sabine Lisicki of Germany celebrates a point during her quarter-final match against Kaia Kanepi of Estonia.
Photograph: Julian Finney/Getty Images
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