Darcy Kuemper made saves on six Vancouver shooters in the tiebreaker until Fontaine finally broke the deadlock by faking a high shot and then sliding the puck underneath the Canucks' Eddie Lack.
Kuemper, who turned aside 30-of-31 shots in regulation and overtime, secured the win with a final stop on David Booth, handing the Wild a fourth straight victory.
Zach Parise got Minnesota's only regulation goal.
Ryan Kesler scored and Lack finished with 22 stops for the Canucks, losers of eight in nine.
2014: The Year in Music [PHOTOS]