Angelique Kerber, the 2018 Wimbledon champion, is into her first WTA final since 2019 having come out on top in the evening semi-final.
Kvitova lost serve three times but hit 10 aces while prevailing against 135th-ranked Piter in just under two hours at the Wimbledon warmup.
The world number 12 pulled out of the French Open last week after tearing a ligament in her left ankle in a freak accident as she walked out of a TV studio in Paris.
No.5 seed Elina Svitolina of Ukraine needed nearly 2.5 hours to beat ninth-seeded Petra Kvitova of the Czech Republic 2-6, 7-5, 7-5 and earn her ticket to the quarterfinals.
On Tuesday, Kvitova, a two-time Wimbledon champion, had to overcome the intense heat and Wickmayer, a US Open semi-finalist in 2009.
Hsieh Su-Wei, who reached a career singles high ranking of 23 in 2013, welcomed the shake-up at the top of the sport.
Serena Williams is ranked 183 after her pregnancy absence and French Open chiefs decided against seeding her.
Grass suited for Serena Williams' style, she will be top contender at Wimbledon: Tennis legend Chris Evert
Evert also believes that Czech Petra Kvitova will be dangerous on grass and has to be considered as the one of the top two-three favorites.
Caroline Wozniacki had to battle hard to book her place in the quarter-finals at the Eastbourne WTA tournament.
Bouchard failed to make it beyond the opening round in two of her last three Wimbledon appearances and in January dropped out of the top 100 for the first time in five years.
Kvitova saw off Rybarikova 4-6, 6-1, 6-2 in a final lasting just over two hours on the grass-courts of the Edgbaston Priory Club.
Former world number one Williams, a three-time champion in Paris, is playing a Grand Slam for the first time since winning the Australian Open in 2017.
Simona Halep retains top spot in WTA rankings, Petra Kvitova moves to eighth following Madrid Open win
Petra Kvitova jumped two spots to eighth in the latest WTA rankings released after beating Kiki Bertens to win the Madrid Open.
Kvitova, who was also the champion in Madrid in 2011 and 2015, has now claimed four titles in 2018 after triumphs in St Petersburg, Doha and last weekend in Prague.