British number one Johanna Konta beat Ukrainian Lesia Tsurenko to reach the second round of the Aegon Classic in Birmingham.
Compared to Konta, Kvitova of the Czech Republic had a relatively easy go in her match against compatriot Tereza Smitkova with a 6-2, 6-3 victory.
The contrast of Cibulkova's intense character and Safarova's calm presence on the court made for a fantastic encounter, with the relentless trade of groundstrokes producing some stunning rallies, thrilling the crowd on the Anne Jones centre court. "But I also want to enjoy each one of them on their own as well", she said.
"She's a very big player", said Konta. But I felt I stayed in each point quite well.
But the 26-year-old, who was reached the final of the Nottingham WTA event before losing on Sunday to Croatian Donna Vekic, is certainly expected to mount a more serious challenge this year. However, Konta found her form at the right time, and eventually came through 8-6 in the second set tie-break.
Konta will face thee victor of the all-American match between Coco Vandeweghe and Christina McHale.
Kvitova, who next meets Britain's Naomi Broady, was content with both her performance and the condition of her hand. It's a handsome grass court here as well, so I'm really enjoying playing on the surface here again.
"So I'm glad that now I can focus on tennis, especially on the grass".
She said: "I think this first match on the grass was pretty good". I had good timing on the court today and I'm happy with the way I played. Nonetheless her serve and forehand still looked strong on the English lawn.
"We are still anxious about the hand, so we are not practising that much. I'm really happy to play on it again and be able to play here in Birmingham". "It was so close to going to a third set".