The match went down to the final doubles rubber which Karolina Pliskova and Barbora Strycova edged from Anastasia Pavlyuchenkova and Elena Vesnina 4-6 6-3 6-2 to secure victory for the Czechs.
Maria Sharapova had earlier put the Russians 2-1 up with a come-from-behind 3-6 6-4 6-2 win over Petra Kvitova in the day's opening singles tie.
But Karolina Pliskova ensured the final would go to the wire after a 6-3 6-4 victory over Anastasia Pavlyuchenkova to level matters at 2-2.
The victory marks a fourth Fed Cup success for the dominant Czech Republic in five years and a ninth in total.
The last country to claim four titles in five years was Russia between 2004 and 2008.
"We are feeling unbelievable, we can't describe it," said an ecstatic Strycova in quotes carried by the Fed Cup website. "I'm speechless because this atmosphere playing at home in front of such a crowd is unbelievable.
"I was believing that we could still do it [after going a set down] and believing in our game which we proved and then we did it at the end.
"This crowd was like a fifth person in our team. We really enjoyed it and I would like to thank to them. They pushed us forward."
Pliskova echoed her teammate's euphoria. "I really enjoyed the whole week with the girls and even now this match was just an unbelievable feeling to play here in Prague and I'm just really happy that we have the trophy again."
Despite ending up on the losing side, World No. 4 Sharapova was positive about the experience of playing in her first Fed Cup final.
"This is one of the few competitions where you're not just playing for yourself and I really felt like I would look over to them and every time they were standing up," she said. "That's the meaning of this event."
For Czech captain Petr Pala, however, it was the sweet taste of success on home turf that will prove most memorable.
"The girls have done it and I'm so happy and proud of them," he said. "It was an incredible day for tennis today with a great audience and I think the first match was just excellent.