Kvitova, the tournament's fifth seed from the Czech Republic, defeated France's Stephanie Cohen-Aloro 6-4, 6-0, while seventh-seeded King beat Germany's Kathrin Woerle 6-3, 6-4.
The 21-year-old King, No. 73 in the world rankings, was successful on 61 percent of her first serves in the 90-minute match with Woerle, ranked 124th.
Kvitova, No. 68, converted 60 percent of her first serves, including a handful of aces. The 19-year-old Kvitova won 92 percent of her first serve points.
Top seed Maria Sharapova of Russia opens play Monday against Shenay Perry.
Venus, SerenaВ reach third roundCazorla hit with injury blow
