Stastny's two goals bookended a powerful performance in the first of the quarter-finals at the Hartwall Arena, with his team mate Craig Smith making three of his five assists in the last 12 minutes to put the game out of reach.
"What happened? We sucked, that's what happened," a disappointed Ilya Kovalchuk told reporters.
Stastny fired the first from Paul Smith's zipped pass and the U.S. never looked back.
T.J. Oshie's wrist shot doubled their advantage and though Alexander Svitov's shot reduced the deficit, the Russians never found the answer to the American game plan.
Russia's Alexander Ovechkin, who only arrived in Helsinki from NHL duty on Wednesday, contributed a goal and an assist, but with Smith in the passing groove the U.S. pulled away easily in the third period.
Co-hosts Finland and Slovakia played out a 4-3 thriller in Helsinki, with the home side edging out the 2012 runners-up thanks to a third-period goal from Juhamatti Aaltonen.
Two goals from Petri Kontiola had the Finns coasting as they raced out to a 3-0 lead in the first period, but goals from Michel Miklik, Andrej Sekera and Tomas Surovy brought Slovakia back level.
Aaltonen then fired what proved to be the winning goal from a Kontiola pass with 11 minutes to go to guarantee the co-hosts a trip to Stockholm and a place in the semi-finals.
In Stockholm, Switzerland's fairytale tournament continued as they edged out the Czech Republic 2-1 to set up a semi-final meeting with the United States.
Denis Hollenstein and Roman Josi scored the goals that gave Switzerland their first semi-final spot since 1998.
Fredrik Pettersson was the hero for co-hosts Sweden as they stunned Canada, scoring the game-winning penalty after a thrilling 2-2 draw in regulation.
Steven Stamkos fired Canada into the lead at the start of the second period with the Swedes a man down after Alexander Edler was ejected on a game misconduct penalty.
Having misfired throughout the tournament, the Swedish offense came good in the final period as the Sedin brothers, Henrik and Daniel, combined to feed Nicklas Danielsson, whose slapshot leveled the scores.
The same trio struck again four minutes later as Danielsson put the Swedes in front for the first time in the game only for Claude Giroux to draw Canada level.
Neither side could find the net in overtime. Canada then could not capitalise on misses by Daniel and Henrik Sedin and Pettersson's goal put the pressure on Jordan Eberle whose miss cost his side a semi-final meeting with Finland on Saturday.
- Ice Hockey
- Sports & Recreation
- Alexander Ovechkin
- Ilya Kovalchuk