Kvitova - beaten by Naomi Osaka in last week's final in Melbourne - showed no ill effects as she beat former world number one Victoria Azarenka 6-2 7-6 (3).
The Czech had to withstand a mini-revival from her opponent in the second set but held on to clinch victory in one hour and 40 minutes.
Kvitova told a press conference: "I've just come from Melbourne and I've hit for the first time in my warm-up. I think I played it very well."
Kvitova was joined in round three by eighth seed Donna Vekic, who beat Russian lucky loser Veronika Kudermetova 6-4 6-3, and veteran Vera Zvonareva, who beat Germany's Julia Goerges 4-6 6-4 6-4.
Maria Sharapova was forced to withdraw from her home tournament following a shoulder injury.
The former world number one had been due to play the number three seed, Daria Kasatkina, for a quarter-final spot.
"I tried to do everything possible to be able to be ready to compete this week, but my right shoulder continues to be an issue for me," she said.
"I will meet with my team of doctors over the next few days to evaluate the situation, and I look forward to returning to completion as soon as possible.
"It was so special to play in front of my home crowd this week and I wish I could have continued competing in this fantastic tournament."
At the Thailand Open in Hua Hin, top seed Garbine Muguruza saw off Mona Barthel in straight sets to book her quarter-final spot.
Spaniard Muguruza won seven of the last eight games to seal a 6-3 7-5 victory against her German opponent.
She will face Ukrainian teenager Dayana Yastremska in the next stage after the number eight seed stormed to victory against Peng Shuai.
Yastremska, 18, won 6-1 6-4 to secure her second quarter-final of the year.
Ajla Tomljanovic, the number six seed, beat Kateryna Kozlova 7-6 6-1, while Saisai Zheng also progressed after a 6-2 6-4 victory over Irina-Camelia Begu.
