She recovered from 5-3 down in the final set to beat Gavrilova 6-7 (4) 6-3 7-6 (5).
Reprieved, Gavrilova stormed to a 6-0 in the tiebreak - and then needed five set points to clinch it.
First, Mladenovic double-faulted going for 4-1 in the tiebreak and when she was serving at match point down at 5-6 Kvitova's widish-looking service return took a net cord, lurched into court and fell dead.
"It such an incredible fight between both of us-and unbelievable match-I'm so happy I won", Safarova said.
It was Safarova s second success against a seed this week, her victory over the ninth-seeded Australian following another in the first round against the third-seeded Slovakian, Dominika Cibulkova, when Safarova saved two match points. She saved both of the break points, but a third one quickly followed for Kvitova, however, a powerful backhand down the line from Mladenovic's racquet forced the error from Kvitova.
Mladenovic s serve at 5-6 looked good enough to win the point and draw her level again, with Kvitova s return appearing about to slide wide.
Asked why she believes she's dominated their rivalry, Kvitova suggested familiarity may be a factor.
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"I was struggling [when serving for the match], feeling a stronger wind and I couldn't hold serve". I love playing finals, I like big matches, and I've missed it over the last six months.
Victor of the Kuala Lumpur title in March, Barty could crack the top 50 - only 18 months after returning to tennis from cricket - by the end of Wimbledon.
But after losing her serve at the start of the second set, Safarova retired due to a thigh strain and exhaustion, having played two long matches in her previous three wins.
Muguruza called for her coach, sought to swing the ball around, and eventually just tried to scrap as best she could.
"It was very close, but I played better than I did before". "I like slicing it around on the grass, and I didn't do much wrong".
"For me it is important to use my slice on the grass and I love coming out here, slicing away and getting a bit of purchase on the ball and I was able to do that and it was really pleasing" she said. Playing just her second tournament of 2017, the Czech star outpaced Kristina Mladenovic, 6-4, 7-6 (5) to reach the final four in Birmingham. Saturday June 24, 2017.
Barty and Muguruza will clash in a contrast of styles for the right to face Daria Gavrilova's quarter-final conqueror Lucie Safarova or dual Wimbledon champion Petra Kvitova in the final. Czech Republic's Petra Kvitova in action against Czech Republic's Lucie Safarova during their semifinal match at the Birmingham Classic tennis tournament at Edgbaston Priory, Birmingham, England.
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