Garcia produced an aggressive performance to down Kvitova and the Czech threatened a comeback in the second set but the Frenchwoman was too hot and closed it out on her second match point.
World number six Pliskova had overcome Kristina Mladenovic's stubborn resistance to put the visitors ahead with a thrilling 6-3 4-6 16-14 win.
Mladenovic will take on double Wimbledon champion Kvitova while world number 23 Garcia will play Pliskova in Sunday's reverse singles as the Czech look to claim a fifth title in six years.
After surrendering the first set in a tiebreak, world number 11 Kvitova fell further behind as she trailed 4-1 in the second set.
She did close the gap to 4-3 before Garcia held her nerve to break again and wrap up victory with a forehand winner.
The highlight of the show, however, was earlier.
In one of the competition's finest rubbers, U.S. Open finalist Pliskova wore down Mladenovic in a nail-biting third set which was the longest ever played in a Fed Cup final.
Pliskova appeared to be cruising towards victory after breezing through the first set but then lost her focus in the second to allow Mladenovic back in the contest.
The Czech served for the match at 5-3 in the decider but lost her composure, Mladenovic breaking back with a forehand winner before levelling for 5-5.
The world number six earned two match points on Mladenovic's serve while leading 9-8, but the Frenchwoman served an ace on the first while Pliskova's forehand flew wide on the second.
Play was interrupted as the Frenchwoman had her left thigh strapped by the trainer before captain Amelie Mauresmo took over the massaging duties at each change of ends.
Pliskova saved a break point at 10-10 but sent a backhand long to concede what had appeared a decisive break in the 23rd game. Yet she broke back immediately with Mladenovic serving for the match.
With the Frenchwoman struggling physically, Pliskova proved she had the stamina to get over the finishing line and she finally wore down her opponent in three hours 48 minutes.
"It's the longest match I have ever played," said Pliskova. "She was serving so well in the third set. Unbelievable match from both of us."
(Writing by Julien Pretot,; Editing by Pritha Sarkar)
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