Playing by far its best game of the tournament, Canada scored the first three goals against a Russian defense full of holes and then traded hard hits with their old for the rest of the contest.
Canada will play either defending champion Sweden or Slovakia in the semifinals.
Getzlaf scored from in close just 2:21 into the game, Dan Boyle added a goal on a long slap shot 10 minutes later and Rick Nash finished off a two-on-one opportunity after a Russian turnover at its own blue line.
Canada took a 4-1 lead after the opening period, having outshot the Russians during the first 20 minutes 21-12.
Neither side scored in the third period, during which officials kept a close eye fearing that an all-out fracas might develop. There were 20 minutes of penalties handed out in the final period.
Russia's Alexander Semin ran Boyle hard into the end boards during the final minute and Boyle then retaliated by kicking Semin's skates out from under him.
Both players were penalized and no further incident occurred as time ran down.
Roberto Luongo, who replaced Martin Brodeur in goal for Canada to start the knockout rounds on Tuesday, made 25 saves.
Although the game brought together the top two stars in the National Hockey League, neither played a big role in the contest.
Russia's Alexander Ovechkin took three shots and did not produce a point. Canada's Sidney Crosby took four shots and was not on the ice when any of his team's goals were scored.