Fak, who was part of Slovenia's mixed relay team that crossed the line first but were demoted to silver due to a technical issue with the Norwegian team in last week's opening event in Ruhpolding, hit 19 out of 20 shots and crossed the line in 46:48.2.
That was seven seconds quicker than Simon Fourcade, the Frenchman having to settle for silver after conceding 21.6 seconds to Fak, who won Olympic sprint bronze for Croatia, on the last 4km lap with Jaroslav Soukup of the Czech Republic picking up bronze.
The home fans were confident of another German gold with Arnd Peiffer leading Andreas Birnbacher by 26.7 seconds after the penultimate shoot.
But Peiffer crumbled, as he did on the anchor leg of the mixed relay, by missing two shots and eventually finishing seventh whilst Birnbacher failed to hit his last target and was forced off the podium by eight tenths of a second by the fast finishing Soukup.
Fak was errant with his first effort in the final standing shoot but had the powers of recovery to deny Fourcade a maiden victory. The Frenchman's sole error with the rifle coming on his final prone shoot.
Fourcade's younger brother Martin's hopes of a third gold medal vanished with five misses while it was also a bad day for the heralded Norwegians with the rifle as defending champion Tarjei Boe missed his first two shots and four in total to finish 18th while Ole Einar Bjornedalen could only hit 15 targets and was outside the top 45.
Slovenian Klemen Bauer and German veteran Michael Greis were looking good for a podium finish entering the range for the last time after hitting their first 15 shots but a missed shot apiece saw them drop to sixth and 11th respectively.
Olympic champion Emil Hegle Svendsen recovered from missing two of his first eight shots to take eighth.