The 29-year-old Greis missed one shot but managed to finish the race first at a time of 54 minutes and 23 seconds.
Norway's Ole Einar Bjorndalen, who swept all four men's biathlon golds in Salt Lake City, missed two shots and had to settle for silver with 16 seconds behind. His 36-year-old countryman Halvard Hanevold finished third in 55:31.9.
"Before the race I would never have thought I could win it with 19 successful shots but during the race the wind changed and the conditions became very difficult (for other athletes)," Greis said.
"I had a great day. It is always every difficult to beat Bjornadalen, but it's not impossible. I'm happy to have won.
"My passion, my heart, my determination made (me) the winner."
Greis, ranked 15th and 16th at the 10m sprint and 12.5km pursuit in Salt Lake City, has been on a rise, currently leading the World Cup standings in 20km individual and 10km sprint.
"I had a great race. My technique and my coach were great, I really enjoyed competing in such great form," he smiled.
Bjorndalen, the five-time Olympic champion, said he was "happy with the silver medal".
"This was my best race since coming to San Sicario, and I haven 't done this well in training. My body was working perfectly, so this is promising for the rest of the Olympics," said Bjorndalen.
"You have to do everything perfect. You need to have a good race and you need to do shooting perfect..And he (Gries) is the best guy today."
Bjorndalen claimed missing gold over 20km didn't bother him. "I have more races to go," he said.
When asked to comment on his chance to better countryman Bjorn Daelie's eight-gold record and become the most titled Winter
Olympian in the world, Bjorndalen said he is only 32 and will go for one or two more Olympics.
"I don't think too much about it. I think it will be difficult, but I will try," he said.
Favorite Frenchman Raphael Poiree, the winner of this season's opening individual race on the World Cup circuit and the World Cup overall leader, ended up 20th among the 88 competitors. The seven-time world champion missed three shots, which gave him three minutes penalty.
As the longest event on the biathlon program, Saturday's race was made all the tougher by the twisting, hilly terrain of the San Sicario course.
Squeezed in between the slopes of the women's Alpine skiing events and the track used for the bobsled, luge and skeleton, the trail is packed with tight turns and plenty of climbing- including an energy sapping 1.5km ascent near the end of each 4km loop.
Biathlon will be contested in five events for men and women.
The men's events include 20km individual, 10km sprint, 12.5km pursuit, 4x7.5km relay and 15km mass start, while the women's events feature 15km individual, 7.5km sprint, 10km pursuit, 4x6km relay and 12.5km mass start.
(Xinhua News Agency February 12, 2006)