The Czech ninth seed needed four set points to seal the first set as menacing dark clouds hovered over Court Two, with her 225th ranked opponent slapping a service return long.
A clearly distracted Stevanovic struggled to forget the incident and ended up being broken after Kvitova's service return kissed the line.
Following a two-hour rain break, Kvitova appeared determined to make her greater firepower count, although the final game turned into an almighty tussle of wills.
After watching three match points disappear thanks to Stevanovic's dogged resilience, Kvitova finally triumphed on her fourth attempt to seal a last-16 showdown with either 2019 U.S. Open champion Bianca Andreescu or Tunisian sixth seed Ons Jabeur.
"I love playing on grass and when my serve is working well I love it even more."
Persons:
Petra Kvitova, Natalija, Stevanovic, Kvitova, Karolina Pliskova, Bianca Andreescu, It's, Pritha Sarkar, Hugh Lawson
Organizations:
Wimbledon, All England Club, Serbian, Hawkeye, Thomson
Locations:
Czech, London, Berlin