After Daria Kasatkina swept to a 6-2 6-4 win over Jil Teichmann to put the Russians ahead against Switzerland, Samsonova produced a high-quality performance to win 3-6 6-3 6-4 against Bencic.
It meant there was no need for a doubles decider, with the Russian squad taking the match 2-0.
Samsonova had not expected to be involved in the singles contest in Prague, but a knee problem forced Anastasia Pavlyuchenkova to pull out just minutes before Sunday's (AEDT) final got under way, forcing Russian captain Igor Andreev into a reshuffle.
A worthy substitute, Samsonova is ranked No.40 in the world, while Bencic sits at No.17, and this win was the Russian's third victory in three meetings this year with the Tokyo 2020 gold medallist.
One of those came in the final of the Berlin grass-court tournament, and the 22-year-old was not over-awed by another big occasion this time.
Just as she did in Berlin, Samsonova lost the opening set but then dominated, and by doing so she secured a fifth Russian triumph in this team competition, previously known as the Fed Cup.
Samsonova said: "I have too many emotions now. It's unbelievable. I'm unbelievably happy. It was an incredible fight. It was a more nervous game. It was more than tennis."
Andreev spoke of the strong bond in his squad, saying: "It's an historical win for us. It's been a long time without any trophies in team tennis. I'm very proud and very happy for the girls, the way they played.
"They're amazing, they're heroes, and they achieved this because they're a team – a real team – and real friends."
Russia dominated this event from 2004 to 2008, winning four of five titles, while Switzerland had only previously been to one final, when Martina Hingis and Patty Schynder were outmatched by Arantxa Sanchez Vicario and Conchita Martinez in the 1998 showpiece.