Peter Prevc of Slovenia, the 2013 world champion, overtook Bardal in the second round to take the silver. Bardal settled for the bronze.
The 26-year-old Stoch jumped 103.5 meters in the second round to give him the best jumps in each round and won by 12.7 points over Prevc.
"I feel like it's really not happened to me. Did this really happen?" Stoch said. "It was a great (first) jump. I didn't know if I won but I knew the result would be good."
Prevc was pleased with second.
"I'm still collecting the best memories of my life," Prevc said. "My performance today was one of the best. I was struggling during training, but I felt confident today and pulled myself together."
Thomas Morgenstern of Austria, returning from serious injuries from a fall during training a month ago, was 14th. Simon Amman of Switzerland, the defending champion from Vancouver in 2010 and who was seeking a record fifth Olympic gold medal, finished 17th.
It was another disappointing result by Austria's Gregor Schlierenzauer, the 2010 bronze medalist, who finished 11th Sunday. He has a record 52 World Cup victories, two Olympic bronzes but no gold.
"I'm really disappointed because the whole year I was talking about the Olympic Games and I couldn't get the best possible result," he said, crying. "The technique wasn't very good and my form was not stable for the whole season."
While the 7,500-seat stadium had only several hundred spectators for some of the training sessions, thousands crowded into the RusSki Gorki Jumping Center for the gold final.
Russian flags were most prominent, but there were also many fans from the jumping-mad countries of Poland, Austria and Slovenia. The locals cheered when word got around the venue that Russia had won its first gold of the games in team figure skating down on the coast.
But one of the biggest roars of the night came when the last of Russia's four jumpers, Mikhail Maksimochkin, took the lead briefly after 23 competitors with one of the best jumps of his career, 104 meters.
Three Americans who qualified for the final didn't make it into the second round when the field was cut to 31. They were Nicholas Alexander of Brattleboro, Vermont (34th place), Peter Frenette of Saranac Lake, N.Y. (45th) and Anders Johnson of Park City, Utah (47th).
Earlier Sunday, Robert Kranjec of Slovenia withdrew from the final after suffering a knee injury in a landing fall during the qualification round on Saturday.
The men's next gold medal is in the large hill on Saturday, followed by the team large hill on Feb. 17.