Second seed Kvitova raced to a 6-1, 6-0 win over Kiki Bertens, the world number 138 from the Netherlands, on Centre Court.
Kvitova, also the 2011 champion, dropped just one point on serve and next meets Kurumi Nara of Japan for a place in the last 32.
"It's great to be back on Centre Court and unbelievable to see all the people clapping," said the Czech, who had been laid low by illness in the week before the tournament.
The powerful 25-year-old left-hander would have been relieved to have enjoyed a brief first round outing as temperatures rocketed to around 30 degrees Celsius.
Wednesday is expected to see a Wimbledon record high of around 35 degrees which would require the heat index, where matches are briefly suspended, to be introduced.
Organisers say the heat rule, which allows for a 10-minute break between the second and third sets of women's matches, can be used when temperatures rise above 30.1 degrees Celsius.
However, the rule which has been adopted by Wimbledon after lobbying from the WTA, does not apply to men even though they have to slug it out over the best of five sets.
Joining Kvitova in the second round was 10th seeded German Angelique Kerber who handed compatriot Carina Witthoeft a 6-0, 6-0 drubbing.
Kerber, a semi-finalist in 2012 and who won the Birmingham tournament on grass in the run-up to Wimbledon, took just 45 minutes to clinch victory, firing 21 winners past the world number 53.
It was the third so-called "double bagel" result of the women's first round.