The duo were roared on by a partisan crowd at the Adler Arena in Sochi as they subdued Sabine Lisicki and Andrea Petkovic 6-2 6-3 in the decisive fifth rubber.
They set up a final showdown with holders the Czech Republic, who thumped France 3-1 in the other semi-final in Ostrava.
Russia needed to win only one of Sunday's rubbers after winning both of the opening day's singles matches.
But that lead vanished as the day progressed, with Petkovic overwhelming Svetlana Kuznetsova 6-2 6-1 before Angelique Kerber drew Germany level by walloping Pavlyuchenkova 6-1 6-0.
Pavlyuchenkova barely had time to recover from that drubbing before she was back on court again for the doubles alongside Vesnina.
She made sure she would not suffer that losing feeling again.
"After I lost my second singles today... I was not really upset, so that was a positive ahead of the doubles," Pavlyuchenkova said.
With Russia losing all four singles sets contested on Sunday, Vesnina and Pavlyuchenkova stopped that run by putting pressure on Lisicki's serve.
Vesnina showed excellent ability from the net, while her ground strokes were equally as impressive.
A fantastic lob by Vesnina set up match point and the Russians pounced on that chance to spark celebrations among the home fans.
Russia, who claimed four titles between 2004 and 2008, will face the Czechs in the Nov 14-15 final.
"It was an unbelievable victory and we are so excited and I am so proud of my team," said a jubilant Vesnina.
(Reporting By Dmitriy Rogovitskiy, editing by Pritha Sarkar)
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