On the game-winning play, the Kings' Trevor Lewis stripped Dan Hamhuis of the puck at center ice and fed it to Stoll, who skated down the left side and unleashed a wrist shot that beat Cory Schneider to the short side.
Brad Richardson tallied 3 1/2 minutes into the third period off a feed from Drew Doughty to forge a 1-1 tie, and Los Angeles went on to upend the top-seeded Canucks 4-games-to-1 in their Western Conference quarterfinal series.
Jonathan Quick turned aside 26-of-27 shots for the eighth-seeded Kings, who won their first post-season series since 2001.
Henrik Sedin scored in the first period for Vancouver, which had finished with the league's best regular-season record.
Schneider made 35 stops for the Canucks.