Stoch had won on the normal hill earlier in the games. He became the fourth athlete in the 2014 Olympics with two individual titles.
He led Japan's Noriaki Kasai by 2.8 points after the first of two rounds of jumping and then barely held on for the gold, winning by 1.3 points. Kasai had the longest jump of the second round at 133.5 meters, one meter farther than Stoch's attempt.
The bronze medal went to Peter Prevc of Slovenia, who finished second to Stoch on the normal hill.
This is the fourth straight Winter Games in which a ski jumper from Poland has won a medal on the large hill, but it is the first gold for that country since Wojciech Fortuna won one at Sapporo in 1972.
The other Olympians with two individual gold medals this year are Dario Cologna of Switzerland in cross-country skiing and both Martin Fourcade of France and Dora Domracheva of Belarus in the biathlon.
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