Stoch, 25, claimed the large hill world title last month, but headed to Poland still searching for his maiden World Cup win of the campaign.
But Stoch will have to wait no more as he finally climbed the top step of the podium, finishing with 268.1 points to do so.
And all that waiting clearly meant that Stoch wanted to make sure of his first World Cup victory in 2013, with the rest of the field finishing some way behind. Daiki Ito of Japan was second, 10.9 points back, with German Severin Freund finishing third on 255.2.
But the day still belonged to Austrian Schlierenzauer as his fifth-place finish was enough to hand him his second overall World Cup crown, his last coming in 2009, as he holds an unassailable lead with four events remaining.
The other World Cup medals are yet to be decided. Stoch's maiden victory moves the Pole onto 747 World Cup points as he sits fifth in the overall standings, 45 behind Norway's Anders Jacobsen who finished down in 35th in Kuopio.
Freund's third place moves him into the same place in the overall standings on 819 points, with Anders Bardal of Norway second on 912 after finishing fourth in Finland.
- Sports & Recreation