Kvitova, the 2011 winner, and five-time champion Venus treated Centre Court fans to a high-quality third round encounter lasting two and a half hours before the Czech sixth seed finally prevailed, extending her impressive record against the 34-year-old American to four wins from their five encounters.
The 24-year-old, who has reached at least the quarter-finals in each of her last four visits to Wimbledon, will play Chinese world number 61 Peng Shuai for a place in the last eight.
Venus's defeat means the seven-time Grand Slam winner has failed to reach the last 16 at a major since Wimbledon in 2011.
"It was definitely a very tough battle. I was preparing for this because I know Venus can play very well on grass. I'm just happy I'm through," Kvitova said.
"When I lost the first set I was a little bit down mentally but I knew I could come back.
"In the third set anything can happen. It was hard to break her. I was just trying to push her and finally I did it. I was just lucky in the end."
Kvitova has failed to reach a Grand Slam final since her Wimbledon triumph, with semi-final appearances at the Australian and French Opens in 2012 her best efforts.
But Wimbledon's grasscourts are where the Czech feels most at home and she believes another strong run could be on the cards this year.
"I'm feeling well. I love to play on grass and I have great memories of 2011 here at Wimbledon," she added.
"I'm pretty confident but everyone is playing well at this stage. I have to focus on each point."
At 34, Venus was the oldest woman left in the Wimbledon singles and, plagued for the last three years by Sjogren's Disease -- an immune system disease that leaves her battling fatigue and joint pain -- and she hasn't won a Grand Slam since securing the last of her seven major titles in 2008 at Wimbledon.
In her 17th Wimbledon appearance, and her 63rd career Grand Slam appearance, Venus had made it to the last 32 at a major for the first time since the 2013 Australian Open and she gave a glimpse of her former glories to push the higher ranked Kvitova all the way.
With the first set finely poised at 5-6, Kvitova was serving to force a tie-break, but Venus stepped on the gas and broke to love to take the opener.
Kvitova refused to be over-powered in the second set and the two big hitters slugged it out from the baseline until the tie-break, which the Czech left-hander took thanks to an ill-timed double fault from Venus on set point.
All four of their previous meetings had also gone the distance and the Czech again landed the knockout blow deep into a tense third set to clinch a memorable win.
- Sports & Recreation
- Venus Williams
- Petra Kvitova