Sweden's Elvira Oeberg took silver and Justine Braisaz-Bouchet of France bronze.
Preuss hit all 20 shots to win in a time of 26 minutes 58.9 seconds, 39.1 seconds ahead of Oeberg, who passed Braisaz-Bouchet late on the final lap to snatch silver by 1.9 seconds after a frenetic sprint to the line.
With the starting positions decided by the result of Friday's sprint race, the athletes set off in perfect conditions, with bright sunshine and a light breeze blowing across the range.
Swiss Lena Haecki-Gross delighted the crowd by taking the lead and engaging in a nerve-jangling battle on the range with Preuss, but a miss on the third shoot and resulting lap of the 150-metre penalty loop allowed her German rival to move ahead.
Preuss, runner-up to Braisaz-Bouchet in the sprint, made the most of that miss, opening up a big lead and calmly rattling off her final five standing shots to turn the final two kilometres into a victory lap as she claimed her first individual world gold.
Despite missing her first, third and fourth shots, Braisaz-Bouchet emerged from the final visit to the range in second place, half a second ahead of Oeberg, but the young Swede shadowed her expertly before blazing past.