The 28-year-old recorded the fastest times over both runs to finish with a combined time of 1:39.799 and secure his first world title.
It was also a first for his country since three-time Olympic medallist Markus Prock took victory in Altenberg in 1996.
Silver went to two-time Junior World Champion Roman Repilov who was 0.062 seconds back while Italy's Dominik Fischnaller won the bronze, 0.120 back.
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Defending champion Felix Loch set a new track record of 49.892 seconds on his first run – which Kindl then improved to 49.823 – but was sixth fastest on his second run and eventually finished in the same position.
Kindl said: "That was amazing! It's more than a dream come true for me. I don't know what else to say – it's just unbelievable!"
Russia's Repilov meanwhile was already turning his attention to next year's Olympic Games in Pyeongchang.
"I'm delighted with silver, but of course I'd have been even happier with gold," he said. "My goal is to be Olympic Champion next year."
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