Towering Czech Kvitova beat Victoria Azarenka in the final last year before going on to win the Wimbledon title.
The only seeded player to fall was number 15
The ninth seed delivered some powerful serves, hitting 14 aces to set up a meeting with another Russian, Anastasia Pavlyuchenkova, in the next round.
"I was feeling good," Williams said. "It's my first tournament in Europe this year and I just hope I can keep up the good form," added the American who has yet to lose in eight clay outings this season.
"I haven't noticed a difference between the blue and the red clay. I think it's the same, it's just you don't get as dirty," added Williams.
The former world number one struggled past Romania's Simona Halep in three sets on Saturday, but crumpled against stronger opposition on Monday falling 6-4 6-1 to 12th seed
Kerber, 24, is in the midst of her breakout season with both her career title coming in 2012 China's