Kvitova withdrew from the French Open after suffering a freak ankle injury during her post-match media duties at Roland Garros.
The two-time Wimbledon champion recovered to get her grass-court season under way in Germany and battled to a 4-6 6-1 6-4 over Polish outsider Piter.
A week before the third grand slam of the year gets started at the All England Club, top seed Kvitova trailed 2-0 in the final set as she struggled with her serve, but broke three times to book a second-round meeting with Ann Li.
Sloane Stephens withdrew ahead of her scheduled match with Laura Siegemund due to a foot injury. Riya Bhatia stepped in with Stephens absent, but Siegemund consigned her to a 2-6 7-6 (7-1) 6-1 defeat.
Angelique Kerber needed only 50 minutes to see the back of Ekaterina Yashina 6-1 6-1 on home soil, grasping all five break-point opportunities.
Kerber will do battle with Anna Blinkova in round two and Jessie Pegula’s next assignment is an encounter with Katerina Siniakova following a 6-1 6-2 defeat of Amandine Hesse.
Blinkova beat Clara Tauson 7-6 (7-4) 4-6 6-2, while Sara Sorribes Tormo saw off Martina Trevisan 6-4 3-6 6-2
Miserable weather in Eastbourne prevented Karolina Pliskova, Madison Keys, Bianca Andreescu and Madison Keys from playing at the Viking International.
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