The three-time Olympic champion posted jumps of 125 and 132.5 meters to finish narrowly behind Germany's winner Karl Geiger.
Marius Lindvik of Norway placed third.
The second-highest placed Pole, Andrzej Stękała, was seventh.
Initially, the Polish team had been excluded from the Four Hills opener after one of its members, Klemens Murańka, tested positive for COVID-19.
At the last minute the Poles were cleared to compete in Oberstdorf by German health authorities after further checks in which all members of the national team tested negative for the coronavirus.
The Four Hills Tournament, which is part of the ski-jumping World Cup circuit, features a series of four competitions taking place in Germany and Austria every year.
The next stop after Oberstdorf is Germany’s Garmisch-Partenkirchen, where the world's top ski jumpers are set to compete on New Year's Day.
After that the series will move to Austria for events in Innsbruck on January 3 and Bischofshofen on January 6.
In January this year, Dawid Kubacki became the third Polish ski jumper to claim the overall Four Hills Tournament title after soaring to victory in the final stage of the annual series in Bischofshofen, Austria.
Poland’s Stoch won the 2017/2018 season’s Four Hills Tournament and also triumphed at the 2016/2017 tournament, ahead of teammate Piotr Żyła and another Pole, Maciej Kot, in fourth place.
Stoch earlier this month came in runner-up at a World Cup event in Engelberg, Switzerland, claiming his first individual podium of the season.
Poland's Żyła on December 20 finished third in the men's ski-jumping event in Engelberg, claiming his 14th career individual World Cup podium.
Earlier this month, Team Poland, comprised of Stoch, Żyła, Kubacki and Stękała, took the bronze at the Ski Flying World Championships in Planica, Slovenia.
Last month, Poland took third place in the World Cup season-opening team competition in their home country, finishing behind winners Germany and runners-up Austria.
The 2020/2021 ski-jumping World Cup circuit features a total of 35 competitions, including six team events, in various countries.
The schedule includes the Raw Air event in Norway in March.
Czech Michal Doležal last year took over as the head coach of the Polish men’s ski-jumping team to replace Austrian Stefan Horngacher.
(gs/pk)
Source: TVP, PAP