After Ana Ivanovic gave the Serbs a 2-1 advantage with a 3-6, 6-0, 6-3 win over Russia's Anastasia Pavlyuchenkova in the day's first match, Jankovic followed through with a decisive victory over Kuznetsova.
After the Serb breezed through the first set, Kuznetsova responded by winning the first three games of the second frame. But Jankovic then stormed back with five straight, putting Serbia into its first Fed Cup final.
It will face the Czech Republic in the November championship, following that country's victory over Italy Sunday.
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