Tolchinski scored Russia's first goal of the game in the second period and followed it up by connecting on a third-period penalty shot after being impeded while on a short-handed breakaway. He completed the hat trick with an empty-net goal that was awarded after a U.S. player threw his stick.
Valeri Nicushkin added two of his own for Russia, including another empty netter, while Nikita Cherepanov and Ivan Barbashev also scored. Evan Allen, Will Butcher, J.T. Compher and Anthony Louis replied for the U.S.
Nikita Serebryakov made 45 saves to pick up the win. Hunter Miska made 27 stops in defeat.
Apart from Tolchinski's empty-net goal, the game included another unusual sequence. Cherepanov's second-period goal came on a dump in from centre ice that hit an American defenceman's stick and bounced over Miska's shoulder.
Tolchinski said the game was the biggest of his young career.
"It was important for us to win this tournament," he said through an interpreter. "This is the biggest tournament that most of us have ever played in and some players may never get an opportunity to play at this level again.
"It was a physical game and the intensity and emotion out there tonight was just amazing. It meant a lot to us because we will likely never play together as a team."
Russian coach Sergei Suyarkov said he never doubted his team's ability to win the tournament.
"We had a tough game last night (in the semifinal against Ontario) and when we won it, I was confident in the ability of our team to come though tonight," said Suyarkov, who also spoke through an interpreter. "The flow of the game tonight was excellent and there were many wonderful players in it.
"We are very happy to have won."
Earlier Wednesday, Max Domi scored twice to lead Ontario past Sweden 5-2 to capture the bronze medal.
Bo Horvat, Nicholas Baptiste and Jordan Subban had the other goals for Ontario. Leon Bristedt scored both goals for Sweden.
The contest began as a tight-checking affair with neither team scoring in the first period. Swedish netminder Ebbe Sionas was replaced midway through the period by Jonas Johansson after starting the contest despite suffering a broken finger in the warmup.
Bristedt opened the scoring in the second, firing a wrist shot past Ontario goalie Spencer Martin after taking a pass from Andre Burkowsky.
Ontario captain Horvat tied it by firing a shot past Johansson off an off-man rush. Bristedt put Sweden back ahead with a slapshot from the top of the circle later in the period.
Ontario cemented the victory with four third-period goals.
Subban tied the score on the power play just 20 seconds into the third before Baptiste gave Ontario its first lead two minutes later with a short-handed goal.
Sionas returned to the game following Baptiste's goal.
Domi put Ontario ahead 4-2 with a power-play goal. He added another insurance goal by converting a backhand to cap a terrific individual effort.
Ontario entered the tournament as the defending champion but Subban said the team was content with its third-place finish.
"Bronze is not what we came here for," he said. "But it is still quite an accomplishment."
Ontario head coach Troy Smith agreed.
"Today's game speaks to the resiliency of our players," he said. "Even with all the injuries and how tired they were, the guys found a way to win.
"We scored some big goals in the third period and (goaltender) Spencer Martin made some big saves throughout the game."
Martin stopped 26 shots for the win.