Czech Kvitova needed just 60 minutes to complete the 6-2 6-2 win and will face American CiCi Bellis next.
The two-time Wimbledon champion only returned to tennis in May after a knife attack that threatened her career.
"It's nice to play somewhere for the first time after so many years on the tour," said the 27-year-old.
"I served very well and I knew that I had to be focused and just play aggressive."
Elsewhere, world number two Simona Halep beat Mariana Duque-Marino of Colombia 3-6 6-4 6-2 as the on-court temperature reached a punishing 47C at the Citi Open in Washington.
"It was really hot out there," said the Romanian, who will play Russian seventh seed Ekaterina Makarova in the quarter-finals.
"I was a little bit dead on the court. It was the same thing for her so I said I have to keep fighting even if I'm struggling."
Halep, 25, needs to reach the final in Washington to have a chance of overtaking Karolina Pliskova for the number one ranking in Toronto next week.
Petra Kvitova powered into the quarter-finals of the Stanford Bank of the West Classic with a straight-set victory over Ukraine's Kateryna Bondarenko.