Kvitova, the Czech No.1, got off to a nervous start against Anastasia Pavlyuchenkova in the opening match, committing 15 unforced errors to help the Russian take the first set 6-2.
The two-time Wimbledon champion settled down after the break and stormed back to grab the next two sets 6-1, 6-1 with the Russian double-faulting on match point.
In the second singles, the world number four Sharapova, playing in her first Fed Cup final, beat Karolina Pliskova 6-3, 6-4, rekindling Russian hopes of winning a first Fed Cup title since 2008.
Kvitova said the support of a raucous home crowd at the O2 Arena had helped her overcome nerves in the first set as the Czechs set out to defend their title and claim their fourth Fed Cup triumph in five years.
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"I was nervous since yesterday just like every time at the beginning of a tournament and it was really difficult to get going," Kvitova said. "I missed some easy balls and it was difficult for me to turn it around."
Sharapova's match against world number six Kvitova on Sunday now becomes pivotal to the outcome and the Russian expects it to be close.
"It's the last match of the season against an opponent I know really well," Sharapova said. "It is just going to come down to a little bit here or there."
After the Kvitova-Sharapova showdown, Pliskova plays Pavlyuchenkova and the title could be decided by the doubles between the Czechs Lucie Safarova and Barbora Strycova and their opponents, Ekaterina Makarova and Elena Vesnina.
(Reporting by Michael Kahn,; Editing by Ian Chadband)
