The 27-year-old Petkovic won 6-2, 6-1 in one hour 21 minutes to record her fourth win over Russia's most successful player in Fed Cup history in their six head-to-head meetings.
Petkovic, who is currently 11th in the WTA rankings, started confidently, breaking her opponent's serve on three occasions to take the opening set in 41 minutes, while Kuznetsova, 29, broke back only once.
In the second Petkovic underlined her supremacy at the red clay court of Sochi's Adler Arena as she produced two more breaks to put her team back on the track.
In the second reversed singles match Russia's Anastasia Pavlyuchenkova will take on Julia Goerges of Germany.
In Sunday's last rubber Elena Vesnina and Vera Zvonareva, a replacement for injured Maria Sharapova, will play Angelique Kerber and Andrea Petkovic in the doubles.
On Saturday Kuznetsova beat Goerges 6-4, 6-4 to put Russia 1-0 into the lead, while Pavlyuchenkova battled back from a set down to defeat Sabine Lisicki to give her country a comfortable 2-0 lead.
In the final the winner of the tie will face the Czech Republic, who had clinched an unassailable 3-0 lead over France in the other semi-final.