The Czech superstar looked shaky in the opening set, committing numerous errors before righting the ship and winning the match 6-7(4) 6-3 6-2 in two hours and 15 minutes.
Having made quick work of Alexandrova in the previous round, the World No.8 faced tougher opposition in Sakkari.
The Greek had upset America's Madison Keys in her third round match, and played some aggressive tennis to steal the first set from Kvitová in just under an hour.
The nerves began to set in however, as Sakkari got broken four times in the second set. Neither lady could develop much rhythm as they exchanged breaks almost every game but Kvitová's experience enabled her to play the big points better and win the second set.
Sakkari eventually succumbed to the 2019 runner-up, with Kvitová hitting 7 winners to none for the rising Greek star. The 7th-seeded Czech closed out the final set after breaking her opponent twice, booking her spot in the quarterfinals.
Kvitová faces a daunting challenge in the next round, potentially clashing with World No.1 Ashleigh Barty or in-form American Alison Riske.
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