"We knew that we will do it if we win," said Kovalchuk, the all-time leading Russian goal-scorer in Olympic play.
Singing the Russian anthem on the field of play is a violation of the IOC's rules on neutrality, which were imposed on Russia as part of sanctions punishing the nation over systematic doping across many sports.
The victory marked the first time a team from Russia have won the gold medal in hockey since 1992, when the so-called Unified Team representing Russia and five other former Soviet republics beat Canada for the Olympic championship.
"It means a lot. We didn't win Olympics since '92," Kovalchuk said. "It was a while ago. That was our dream. That was my dream for when I was five years old, when I started playing. It's great and it feels good."
The game was a thriller from the start and ended with flair, a perfect one-time slap shot from Kaprizov that ripped past German goaltender Danny aus den Birken with Germany's Patrick Reimer off for high sticking.
Kaprizov had been fed the puck by the other Russian hero of the game, Gusev, who netted two third period goals, including the one that tied it, sending the game to overtime with less than a minute to go and the Germans looking like they were about to pull off a huge upset. Gusev finished as the Olympic tournament's points leader with four goals and eight assists.
The Russians found themselves evenly matched by a German team who surprised the hockey world by making it to their first Olympic final. With the loss, the Germans won silver, their best finish ever in Olympic ice hockey and their first medal since a bronze at the Innsbruck games in 1976.
On paper the final shouldn't have been a fair fight, but the Germans, playing hockey for a country primarily obsessed with football, skated evenly with the OAR, a team loaded with top home-grown talent from Russia's Kontinental Hockey League, seen as the world's second-best league after the NHL, and led by ex-NHL all stars Pavel Datsyuk, their captain, and Kovalchuk.
The Germans had punched above their weight to get to the final, beating hockey powerhouses Sweden and Canada, and they were not about to quit with the gold medal on the line.
They came back twice from one-goal deficits and took the lead late on a goal by Jonas Muller, who beat Vasili Koshechkin between the legs, only to have their hearts broken by Gusev and Kaprizov.
"It's a little tough right now because we all felt we could have won that game, but that's hockey, that's just the way it is," German coach Marco Sturm said. "We all thought we would sit at home and watch the final on the couch. But here we are. The boys are going to bring silver home and they should be proud."
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