The hosts, buoyed by a partisan crowd at the E Center, scored three early goals, all from power plays, and seemed to be coasting to a comfortable win.
However, Russia came out in the third period a changed outfit and scored two goals within three minutes to set up a grandstand finish.
Having been completely outplayed for 40 minutes, the Russians threw everything at Mike Richter's goal, but were unable to find a way through for the vital third goal.
The match came 22 years to the day since their meeting at the Lake Placid games - one of the most memorable hockey matches in history.
This Olympic meeting paled in comparison until the Russians came out for the third period and finally started to play.
In the opening two periods the Americans played with aggression and confidence against lacklustre opponents.
Bill Guerin, Scott Young and Phil Housely all scored on power plays to give the US a 3-0 lead after 17:42 of the second period.
Their dominance was overwhelming and they outshot their opponents 38-11 in the first two periods.
Guerin pushed in a rebound for the first goal after 15:56 of the first period - the first time Nikolai Khabibulin had been beaten in 60 shots following his shut-out against the Czechs.
The US maintained their momentum into the second period.
Scott Young made it two on seven minutes, deflecting Housley's shot over the committed Khabibulin.
And 10 minutes later provider turned poacher, Housley shooting in having been given space.
But having mustered only four and seven shots in each of the first two periods, Russia took control of the game on the resumption.
In the third period they had 19 shots on goal, scoring twice.
The first came within 11 seconds from Alexei Kovalev and after 3:21 Vladimir Malakhov added a second.
But Malakhov's New York rangers team-mate Richter was in outstanding form and kept his team in the game with a string of superb saves.
Richter made 16 of his 27 match saves in the third period, the most vital coming in a Russian power play.
The US goal was under siege with Russian skaters repeatedly surging forward and beyond a shapeless defence.
But Richter was on hand, sensationally turning aside Sergei Samsonov on one side of the net, before palming Alexei Yashin on the other.
Russia's desperation was reminiscent of the Lake Placid encounter, but history repeated itself and the hosts held on for victory to the delight, and relief, of the majority of the crowd.
The US will now face Canada in Sunday's final - a re-match of Thursday's women's gold medal game.