Norway's Robert Johansson picked up a second bronze to go with the one he won in the normal hill one week earlier.
After hurtling down the floodlit 142-metre ramp, taking off at 90 km/h and executing an immaculate jump and landing, Stoch bit on his glove as he endured a short but nervous wait for the judges' scores.
He told reporters he rated his performance even higher than when he won the same event for the first time in Sochi four years ago.
"Sochi was amazing too, but this today was outstanding," he said. "Many jumpers showed their best performance. I'm more satisfied with the work I did today."
The Pole ended on 285.7 points, with Wellinger - winner of the smaller normal hill competition a week ago - on 282.3 and Johansson, last week's bronze medallist, on 275.3.
The German actually beat Stoch for distance in both rounds - 135.5 and 142 metres to 135 and 136.5 - but the Pole scored higher when the jumps were adjusted for prevailing wind conditions, and he earned an extra judges' point on round one.
Wellinger said he had felt relaxed after playing football in an underground car park during the afternoon and was now looking forward to Monday's team competition, when all three medallists will resume their rivalry.
"It's fantastic that the whole team is performing at a high level. We have four guys among the eight best," said Johansson, whose handlebar moustache would win the gold medal if cultivating facial hair was ever to become an elite sport.
"To be able to be in the medals on Monday your team needs eight quite fantastic jumps, so let's see what happens."
Norway, with no gold in this event since 1964, held first, second and third positions through Johansson, Daniel Andre Tande and Johann Andre Forfang before Wellinger soared in front of them.
Stoch's victory marked a return to form after he managed only fourth in the normal hill here a week ago.
He is the fourth ski jumper to win two Olympic gold medals on the large hill after Birger Ruud of Norway, Matti Nykanen of Finland and Simon Ammann of Switzerland, who finished 13th on Saturday.
Taking part in his eighth Winter Olympics - an outright record - at the age of 45, Japan's Noriaki Kasai, the silver medallist in Sochi, came 33rd in the first round and failed to make it through to the second.
(Reporting by Mark Trevelyan; editing by Clare Lovell, Neville Dalton)
