The duo also met at the last year's championships when the Czech ninth seed came on top in another three-setter.
Paolini found some momentum and made Kvitova work in the second set but the experienced Czech comfortably took the third, firing eight aces and 36 winners throughout the match.
"I was trying hard in the second set to break her but this didn't happen.
In the third I got an opportunity and I made it, and I think that since then I just kept going," Kvitova said.
The 33-year-old will face the winner of unseeded pair Aliaksandra Sasnovich v Nuria Parrizas Diaz in the second round.
Persons:
Petra Kvitova, Italy's Jasmine Paolini REUTERS, Dylan Martinez, Italy's Jasmine Paolini, Kvitova, I've, it's, Paolini, Nuria Parrizas Diaz, Anita Kobylinska, Toby Davis
Organizations:
Lawn Tennis, Croquet Club, Dylan Martinez LONDON, Wimbledon, Centre Court, Thomson
Locations:
London, Britain, Czech, Gdansk