The convincing victory moved the Russians directly into the quarter-final round, giving them an extra day of rest and cementing their credentials as one of the tournament favourites, despite a surprise opening loss to Slovakia. The Americans will have to play in a qualification playoff on Tuesday.
Kovalchuk's goals came 29 seconds apart on either side of the second intermission and proved to be the back breakers in a game the Americans had hung close in despite getting out-hit and finding themselves repeatedly on the defensive.
The former NHL all star's first came with one second remaining in the second period and he got his second inside the first 30 seconds of the third, rifling a shot over U.S. goaltender Ryan Zapolski's left shoulder and into the top of the net.
With the two goals, Kovalchuk, who now plays in the Russian-based Kontinental Hockey League, became the top scoring Russian Olympian ever. His 13 career Olympic goals top Pavel Bure's previous record of 11.
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"I still have some gas left in my tank, so I hope I score some more," Kovalchuk said.
"I think we played well. We came out strong. We scored the first goal then our goalie made some great saves."
Prokhorkin, who was drafted by the NHL's Los Angeles Kings but has never played there, opened the scoring in the first period for the Russians, redirecting a hard feed from Sergei Mozyakin as he was crossing in front of the U.S. goal. His second came early in the second.
It was a physical game from the moment the puck dropped, with the Russians, pound for pound a bigger team, levelling a hit on an American each time a U.S. player touched the puck.
They set their sights repeatedly on the biggest American player, Jordan Greenway, and he found himself in more than one extended shoving match with a Russian, including one in front of the Russian bench with Alexander Barabanov in the first period.
"He didn't want to let go of me," Greenway said. "He wanted to do a little dance with me by the bench, so I was willing to do it."
It is a rivalry that has held outsized importance ever since a group of American college players toppled the mighty Soviet team at the 1980 Olympics in Lake Placid.
In six Olympic meetings since then, including Saturday's victory, the Russians hold the series lead, winning four times, losing once and tying once. Saturday's win avenges a 3-2 shootout loss to the Americans in Sochi, where the Russians were hosts.
The U.S. had chances, however.
Ryan Donato, who scored two goals against the Slovaks on Friday, ripped a wrist shot off the cross bar behind Russian goaltender Vasili Koshechkin, and the Americans caught a couple of other unlucky posts.
U.S. captain Brian Gionta missed a chance to bring the U.S. back to within one on a breakaway in the second period. He had Koshechkin beaten but the puck slid off the toe of his stick.
"We had a couple of really good looks, myself included," Gionta said. "We get a couple of those, it's a different game going into third."
"It's tough when we can't score," Zapolski said. "It's a little bit frustrating... I think we did a lot of good things again, but we've just got to find a way to score some more goals and have more pressure down there."
(Reporting By Dan Burns; editing by Clare Lovell)
