Sweden, which took 2014 silver at Sochi, defeated Finland 3-1 while the Czech Republic downed Switzerland 4-1 and the Canadians blanked South Korea 4-0 to book a last-eight date.
“It's a big win,” Sweden's Joel Lundqvist said. “We played really well. We were just battling out there.”
Together with the Olympic Athletes from Russia, seeking the first Olympic gold for Russian talent since 1992, they will enjoy a break until Wednesday's tension-packed knockout quarter-finals.
“For sure it's one of the scariest games of the Olympics,” Czech veteran Martin Erat said. “You work to get there and if you don't win, you don't get anything and you go home.”
The United States and Finland could be ousted before the quarter-finals. They are among eight teams who face knockout matches Tuesday to decide the other four spots in the quarter-finals.
“Now it gets real,” Czech assistant coach Jaroslav Modry said.
The Americans will face Slovakia, whom they edged 2-1 in group play thanks to two goals from Harvard University star Ryan Donato. The winner meets the Czechs in the quarter-finals.
Canada's quarter-final foe will be the Finland-South Korea winner while Sweden awaits either Germany or Switzerland.
“We have a very important game coming up for sure,” Lundqvist said. “We're happy so far but if we lose the quarter-final it will be so disappointing.”
Patrik Zackrisson broke a 1-1 deadlock with 11:07 remaining in the third period to lift Sweden to victory, Oscar Maller adding an empty-net tally five seconds from the end to seal Finland's fate.