Playing before the Slovak hometown crowd in the quarterfinals series, Petkovic saved match point in a second-set tie-breaker and went on to stun Cibulkova 2-6, 7-6 (9-7), 6-2.
Cibulkova was playing her first match since losing to Li Na in the finals of the Australian Open last month.
She was victimized by 10 service aces from Petkovic, who ran up her record in Fed Cup singles rubbers to seven wins in eight matches.
Angelique Kerber also won Saturday, to give Germany a 2-0 lead in the series, which they can clinch Sunday in reverse singles. Kerber beat Daniela Hantuchova 7-6 (11-9), 6-1 and will face Cibulkova Sunday.
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