Petra Kvitova stays on track for third Wimbledon title after Natalija Stevanovic victory
The Czech former world number two has pedigree on grass but has only made it past the third round once since she claimed her second title at the All England Club in 2014.
The ninth seed, who warmed up for Wimbledon by winning the WTA tournament on grass in Berlin last month, swapped early breaks with Stevanovic but broke again to love in the sixth game, which proved decisive.
Both players were vulnerable on serve in the second set and were locked at 4-4 after a fourth break.
World number 225 Stevanovic held to edge ahead 5-4 before rain swept across the courts, forcing a lengthy delay.
When they returned, Kvitova won 10 consecutive points but she struggled to close the deal against stubborn Stevanovic before finally sealing the victory on her fourth match point.
"I love playing on grass, for sure," said Kvitova. "When my serve is working I love it even more.
"I don't think it was the case today but somehow I found a way, which I'm very happy with."
