Germany held a narrow lead at halfway, but excellent efforts from Michael Hayboeck and Daniel Huber gave Austria an advantage of 3.5 points with one jump to go.
And Kraft won his personal head-to-head with Markus Eisenbichler to ensure the Austrian quartet stood atop the podium at the start of the 2020/21 campaign.
"We knew that if we all did good jumps and repeated our training jumps in the competition, we could be far ahead or compete with the best. I think that was a really great job from us." - Daniel Huber to FIS Ski Jumping
Huber the hero for Austria
There was very little to choose between Poland, Austria, and Germany at the start of the competition.
Kubacki jumped 131.5m but Germany's Karl Geiger matched that distance and Huber was just behind with 131.0m in the first round.
Poland led after three jumps, but Stoch's opening distance of 118.5m saw them drop to third with the other two nations setting an impeccably high standard.
The final leap of the first round, a 123.5m effort from Markus Eisenbichler scoring 134.7 points, saw Germany lead Austria by just 0.7 at halfway.
The Austrians went back into the lead thanks to a 131.5m jump from Hayboeck against Constantin Schmid who managed just 119.0m.
Huber took advantage of the conditions to post a massive distance of 135.0m but Geiger responded with 130.0m which, in receipt of greater wind compensation, yielded a score just a point shy of the Austrian's.
Going into the final set of jumps, Austria led Germany by 3.5 points with it all coming down to Eisenbichler and two-time world champion Kraft.
Eisenbichler looked a little unsteady as he jumped 127.0m, and Kraft matched that distance with greater style points to secure the win for Austria by 8.7 points.
The first individual large hill event of the season takes place on Sunday with Stoch leading the way in qualifying.