With the best-of-five tie locked at 2-2, the US duo eased to a 6-3, 6-1 victory in front of cheering crowds on the indoor hard court in Birmingham, Alabama.
The Americans, who have a record 17 Fed Cup titles but have not lifted the trophy since 2000, will host holders Italy in November in a re-match of last year's final.
The Italians crushed Czech Republic 5-0 in their semifinal in Rome earlier on Sunday.
Earlier, Mattek-Sands had kept American hopes alive by battling past Ekaterina Makarova 6-4, 2-6, 6-3 after Dementieva had beaten Melanie Oudin to give Russia a 2-1 lead.
Ranked 129th, Mattek-Sands broke world number 62 Makarova three times in the final set of the reverse singles encounter before wrapping up victory in just over two-and-a-half hours.
Continually cheered on by loud chants of "USA, USA, USA" from the partisan crowd, Mattek-Sands threw her racket and both arms into the air in celebration after the match ended with the Russian left-hander hitting a forehand long.
"It is great playing in the US, having the home crowd," the American said.
World number six Dementieva had earlier fended off a gritty fightback by Oudin in the first reverse singles to put Russia ahead. Neither player held serve for the first 10 games before an error-strewn first set went into a tiebreak which Dementieva clinched 7-4 after winning the last four points.
Baseliner Oudin, shouldering the burden of being America's number one after Serena and Venus Williams declared themselves unavailable, then broke the erratic Russian in the first, third and fifth games of the second set to level the match.
Although Dementieva was again broken in the third game of the final set to trail 1-2, she won the next four games before sealing victory when Oudin hit a forehand long.
The Russians, winners of four Fed Cup titles between 2004 and 2008, were also under-strength having lost world number three Dinara Safina, fifth-ranked Svetlana Kuznetsova and Maria Sharapova (14) to various injuries this year.
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