A right thigh strain caused Kvitova to withdraw before her quarterfinal match against Heather Watson last week in Eastbourne, so her form in her Wimbledon opener would show if she has recovered and if she is a contender this fortnight.
Hlavackova was making her first Grand Slam main draw appearance since last year's Wimbledon and took an 0-5 record against Top 10 opponents into this encounter.
The Turning Point
The players traded holds through seven games before Kvitova went on a tear. She got the first set's only break during a run of nine straight games and finished off her 6-3, 6-0 victory in style with an ace. It was her 20th win at Wimbledon and her 30th WTA win on grass.
By The Numbers
Kvitova dominated the statistics, including winning 63% of second serve points compared to 27% for Hlavackova and 64% of net points compared to 30%. She was also on top in winners, 29 to 14.
Kvitova broke serve four times, while also saving all three of Hlavackova's break points.
"Andrea played well," Kvitova said. "It was our first meeting in a long time. It's not easy to play Czech girls. I was expecting a tough match and I'm just glad that I won the last point.
"I feel better, which is nice news. I had to pull out of Eastbourne to be ready for Wimbledon, so I'm just glad that it's getting better."