Ziobro claimed his maiden World Cup win in Switzerland while second place for teammate and Polish captain Kamil Stoch moved him into the overall lead.
A jump of 134m put Ziobro into the lead after round one and he coped with the pressure second time out to leap 141m for a winning points total of 275.4.
Stoch, who moves eight points clear of Gregor Schlierenzauer in the World Cup standings, was second with 269.2 while Anders Bardal was third with 268.3.
Ziobro's previous best was a ninth at the season opener in Klingenthal and, with one more event still to come in Engelberg, he wants to repeat his performance.
"I am very happy. I jumped very well and I feel great," he said. "There was a little bit of pressure ahead of the second jump but on the hill I felt I could do it.
"I felt that it was my day. The next day I just want two good jumps."