After a scoreless first period, Finland broke the game open in the second with goals from Tommi Kivisto, Leo Komarov and Mika Pyorala before Jarno Koskiranta capped the scoring when he found the net early in the third.
The loss marked the first defeat for Canada at the world championships since falling to Finland in the quarter-finals of the 2014 edition.
With the win, undefeated Finland advance to play Denmark while Canada will face Sweden in a pair of quarter-final games on Thursday.
In other Group B action, the United States lost 3-2 to Slovakia but still advanced to Thursday's quarter-finals, where they will play Group A winners the Czech Republic.
Belarus avoided bottom spot after they beat France 3-0 meaning Hungary will be relegated from the top level of the world championship for next season.
Meanwhile in Group A, the Czech Republic withstood a late rally by Switzerland for a 5-4 victory to clinch top spot. The Swiss got a pair of goals in the final five minutes to pull within one but the Czechs managed to hang on for the win.
"We knew they were going to play hard, but for us it was an important game as well," Czech winger David Pastrnak told the International Ice Hockey Federation's (IIHF) website.
"We wanted to win the group and go into the quarter-finals with confidence. I think we did a pretty good job. Obviously there were some tough moments, but we just need to continue playing well."
Hosts Russia beat Sweden 4-1 for their sixth consecutive victory to finish second in Group A and will next face Germany in the last eight.
In the final Group A match, Norway's 3-1 win against Latvia ensures they finish in fifth place, one spot above Switzerland.
(Editing by Frank Pingue)
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