The Czech's previous best in the World Cup was a second-placed finish in Willingen in February 2012, but he went one better in Germany this time around.
Koudelka gave a sign of things to come when he topped qualification at the Vogtland Arena on Friday.
And the 25-year-old continued that form in his first jump as 133.6 points left him fourth in the rankings.
A superb jump on the second run resulted in a score of 142.8 points and a combined total of 276.4.
Austria's Stefan Kraft enjoyed a consistent day, finishing third and second respectively in his two attempts, and a score of 274.1 was enough for second place.
Andreas Wellinger gave the home fans hope of a German victory when he led at the halfway stage thanks to a first-jump score of 139.5.
However, he struggled for distance on his second run, recording just 133.5 metres and he had to settle for third.
Norway's Anders Fannemel and Peter Prevc of Slovenia - who finished runner-up in the overall standings last season - completed the top five.
Elsewhere, there was disappointment for defending World Cup champion Kamil Stoch who was unable to compete due to an ankle injury.
The season now moves on to Ruka in Finland, where the second meet of the season takes place next weekend.