Kvitova was tested before getting past Donna Vekic, while 2017 runner-up Wozniacki was also challenged in the third round.
It was a good day for the seeds at the WTA Premier event, but not so for Japanese star Osaka.
The two-time grand slam champion fell to a surprise loss to fellow seed Hsieh Su-wei.
KVITOVA, WOZNIACKI GET THROUGH
Kvitova survived a huge test against Vekic, progressing thanks to a 6-4 3-6 6-4 victory.
The Czech third seed lost to Croatian Vekic when they met in St Petersburg earlier this year, but a single break in the final set proved decisive.
Wozniacki is well-placed for another deep run after overcoming qualifier Monica Niculescu 6-4 7-6 (7-4).
With Osaka’s shock loss, the top half of the draw has opened up for Wozniacki.
OSAKA STUNNED
Osaka had won her previous two meetings with Hsieh, but the 33-year-old claimed a surprise 4-6 7-6 (7-4) 6-3 win.
The 21-year-old Osaka was up a set and a break, only to give up her advantage before losing four straight points in the second-set tie-break.
Osaka took a 2-0 lead in the decider, but lost four straight games from 3-2 up to make an early exit.
ANDREESCU CONTINUES WINNING RUN
Indian Wells champion Bianca Andreescu is in red-hot form.
The Canadian teenager extended her winning streak by beating Angelique Kerber 6-4 4-6 6-1 for her 10th straight victory in what was a repeat of the Indian Wells final.
Anett Kontaveit, Caroline Garcia, Ashleigh Barty and Kiki Bertens were also among the winners on Saturday.
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