Eighth seed Kvitova, who withdrew from the Eastbourne tournament last week with a hamstring injury, appeared to be moving well but looked pale and drawn particularly in the first set.
Kvitova, 28, has worked hard this year, winning five titles. The Czech, Wimbledon champion in 2011 and 2014, won back to back tournaments in Prague and Madrid, and successfully defended her title on grass in Birmingham last month.
Sasnovich, 24, kept her cool throughout the two hour 14 minute match. She went for her shots, served with pace and variety and played big points apparently without nerves.
That was until the 10th game of the second set, when, serving to stay in the set, she started to feel the pressure.
She served two double faults to give big-hitting Kvitova set point and though she saved that one, she lost the set with a forehand out wide.
The wobble seemed to galvanise the Belarusian, however.
She came out fighting in the third set, capturing game after game with steady defence and exquisite shot-making, including drop-shot winners and getting the better of a volley rally at the net.
Kvitova, by contrast, showed only flashes of her old grasscourt brilliance and produced 36 unforced errors. She sent down aces but missed simple forehands and was troubled by the wind as well as her own lack of composure.
Sasnovich completed victory with two aces in a fitting end to a fine performance.
"It was a good match but I can play better as well," Sasnovich said. "I was just warming up when the match was 5-0."
(Reporting by Clare Lovell, editing by Ed Osmondl)
