"Karolina is a great player, and I have a lot of respect for her," Rybarikova, the 2009 winner in Birmingham, said courtside.
"Today I don't think it was her best day, but it was all about serves and returns and I was just better at that. That was the key.
"I put so many returns in, and maybe she was thinking about our last match in Wimbledon. It could have been a different result today, but I'm so happy that I won this match."
Rybarikova will face Kristina Mladenovic for a place in the quarter-finals after the Frenchwoman edged past Czech Katerina Siniakova 1-6 6-2 6-4.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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