Venus Williams, who didn't drop a single set in the Taiwan Open, saved six of nine break points in what was her first meeting against the second-seeded Misaki Doi of Japan.
Czech seventh seed Kvitova fought off Japan's tenacious 92nd-ranked Misaki Doi 6-2, 3-6, 6-1 while Ivanovic dispatched Georgia's Anna Tatishvili 6-2, 6-0.
Dominant world number two Maria Sharapova became the first person to score two double bagel Grand Slam wins in a row since 1985 on Wednesday, but said statistics were not important.
Comeback German girl Andrea Petkovic toppled top seed Nina Bratchikova of Russia while Japanese veteran Kimiko Date-Krumm shocked compatriot and second seed Misaki Doi to storm into the semifinals of the WTA Indian Open, on Friday.
Zheng Jie of China overcame the rain and an intensive schedule to beat Roberta Vinci 6-3, 5-7, 6-4 and reach the semifinals of the Aegon Classic on Saturday.
Top-seeded Samantha Stosur easily reached the Japan Open quarterfinals with a 6-2, 6-4 victory over Misaki Doi on Thursday.
Up-and-coming Misaki Doi gave Japan a perfect start as they led 2-0 against Argentina on the first day of the Fed Cup World Group II play-off on Saturday.
Japanese qualifier Misaki Doi made a dream debut at Wimbledon as the world number 133 clinched a surprise 6-4, 5-7, 7-5 win over 30th seed Bethanie Mattek-Sands in the first round on Wednesday.