Groenefeld put the Germany up, 1-0, with a 6-2, 6-2 win over Lucie Safarova in the day's first match, and later, Kvitova beat Andrea Petkovic, evening the event heading into Sunday's doubles between Lucie Hradecka and Kveta Peschke for the Czechs and the German duo of Tatjana Malek and Kristina Barrois.
Also Sunday, Safarova and Petkovic meet in the first of two reverse singles matches, with Kvitova and Groenefeld squaring off in the nightcap.
The Czechs are five-time Fed Cup champs, while the Germans have won the title twice.
Germany is just 1-4 all-time in Fed Cup play against the Czechs.
The winner plays either Ukraine or Italy in the semifinals.
Notable deaths of 2014 [PHOTOS]