The German, who is seeded ninth, stunned the former champion on Tuesday with a gruelling three-set triumph.
"It's unbelievable," Kerber told BBC Sport. "It was such a tough match, playing to a high level, and it was so close.
"I'm so happy. She's a great player on grass, but I was just focusing on myself and I'm so happy to be in the quarters."
Waiting for Kerber in the quarter-finals will be Canadian 13th seed Eugenie Bouchard.