The Belgium former world number one, preparing for her first Wimbledon since 2006 after coming out of retirement last year, was in scintillating form in the seaside sunshine, making light work of her Czech opponent.
"It was a good one, wasn't it? It's a good sign, a good feeling," Clijsters said.
"I'm playing good tennis, that's the most important thing. It's important not to be too tired. I want to keep this level. I've played two matches well, I want to keep that going, I want to stay mentally focused," she added.
Clijsters, who has never got past the semi-finals at Wimbledon, will face Victoria Azarenka of Belarus in the last eight after she easily beat British qualifier Heather Watson.
French Open runner-up Samantha Stosur also reached the last eight, although she had a tough time against Slovakia's Daniella Hantuchova before winning 6-3, 3-6, 6-4 in breezy conditions.
"Considering the conditions out there, we played a good quality match," Stosur told reporters.
"Grass is difficult sometimes, you add the wind and everything else. It is what it is, it's good to get as many matches as possible," she added.
Former U.S. Open and French Open champion Svetlana Kuznetsova, bidding to rediscover some form before Wimbledon, survived an epic tussle against Romania's Sorana Cirstea before winning 4-6, 7-6, 7-6.
Kuznetsova will face fellow Russian Ekaterina Makarova in the quarter-finals.
There were two encouraging results for British players before the Wimbledon fortnight starting next week.
Elena Baltacha beat China's Zheng Jie 6-2, 1-6, 6-3 to set up a last eight encounter with Stosur while in the men's event James Ward, who on Tuesday eliminated second seed Feliciano Lopez, overcame Germany's Rainer Schuettler 6-3, 7-5.
Top seed Nicolas Almagro bowed out, retiring when a set down against Denis Istomin.Svetlana who?
Bhupathi's mixed doubles campaign over
Federer strolls into Qatar semis
Clijsters hopes to return
Ivanovic eases into quarter finals in Beijing