Compatriot Uschi Disl raced to silver while Sweden's Magdalena Forsberg took bronze.
Wilhelm, who wore a red hat and sported dyed red hair, was in superb form for start to finish.
"I had the best shooting time of my life"
She accurately hit all of her 10 shots in the two shooting sections and reached the finish line in a time of 20 minutes 41.4 seconds - 15.6 seconds ahead Disl.
Disl, who was deemed to be better than her teammate, suffered a 150m penalty lap after missing the target on her second round of shooting.
Swedish World Cup champion and hot favourite for gold, Forsberg, missed one of her five shots and the subesquent penalty lap cost her the chance of winning gold.
Afterwards, Wilhelm paid tribute to Olympic 15km biathlon gold medal winner and fellow German Andrea Henkel.
"I am really satisfied to win this gold medal," said Wilhelm.
"I had the best shooting time of my life, and the victory of Andrea in the last race was a motivation for our team."
Forsberg, who has dominated the World Cup circuit for the last five years, remained positive despite underachieving.
"When I missed one shot during the first round I knew I couldn't go for the gold," she said.
"Still, I just had to go as fast as I could and I gave it my best. I am happy with the bronze."