No.14 seed Kvitova, a two-time Wimbledon champion, eased past last remaining Brit Harriet Dart 6-3, 6-4 in 1 hour and 25 minutes of play.
Earlier, No.12 seed Giorgi of Italy won the first quarterfinal of the day, cruising past lucky loser Viktoriya Tomova of Bulgaria 6-2, 6-1 in just over an hour.
In their first meeting, Kvitova was a force to be reckoned with behind her delivery. The Czech, who won her two Wimbledon titles in 2011 and 2014, hit eight aces and was never broken. Kvitova faced just one break point, which came in the very last game of the match.
"I'm always trying to serve well; sometimes it's working more, sometimes it's not," Kvitova said.
"Today I didn't have a weak game, so it was nice to have for sure, especially at the end of the match when it's always tough to close it out."
Making her seventh appearance in Eastbourne, Kvitova is into the Rothesay International semifinals for just the second time in her career. She lost to Marion Bartoli in the 2011 Eastbourne final, mere weeks before Kvitova claimed her breakthrough major at Wimbledon.
World No.128 Tomova entered the main draw after Ons Jabeur withdrew from singles, and she made the most of it. The Bulgarian won back-to-back tour-level matches for the first time this year, reaching her first WTA 500 quarterfinal by defeating Kirsten Flipkens. Flipkens had beaten Tomova in qualifying just days before.
But the Bulgarian's run was swiftly stopped by World No.26 Giorgi, who was commanding throughout their first meeting. Giorgi fired five aces, won 82 percent of points behind her first serve, and claimed two-thirds of points when returning the Tomova second service.
With the victory, Giorgi matched her Eastbourne semifinal result from last year, and is one win away from her first trip to the Rothesay International final. The Italian has three singles titles on her resume, and her first career title came on grass at 's-Hertogenbosch in 2015.