Three-time Olympic champion from Poland was unfazed by windy conditions as he sealed a sixth individual Four Hills victory.
Windy conditions made it a tricky competition at the Bergisel stadium, which hosted ski jumping at the 1964 and 1976 Winter Olympic Games.
In addition to this, pressure was mounting on the three-time Olympic champion Stoch, who failed to make the podium in last week's Garmisch-Partenkirchen event.
But in Innsbruck, the 33-year-old used all of his experience to take a first-round lead with 127.5m, before sealing victory with a final round 130m.
An almost perfect score of 19.5 out of 20 for style on the winning leap summed up his superior class on this leg.
Victory for his compatriot Stoch came despite admitting to nerves.
After the win, he told FIS, "It was difficult, because I was struggling with basic things and I was nervous.
"Anyway, I'm very happy. I need to be much more focused on myself."
Stoch's victory means he extends his overall lead in this year's event by 15 points, with Kubacki leading the chasing pack as the jumpers head to the fourth and final leg in Bischofshofen on 6 January.
Victory there will see Stoch claim a third overall Four Hills title.