The underdog Kings took the best-of-seven series 4-1, spoiling Vancouver's hopes of a return to the Stanley Cup final.
Stoll scored on a wrist shot from the wing on a turnover at the Canucks' blue-line. The L.A. forward skated in on a 2-on-1, but took the shot himself, picking the top-left corner behind Vancouver goalie Cory Schneider.
"It's special," said Stoll. "It's pride in the organization, and your team and your teammates and coaching staff. They're a great team over there, it took a lot to beat them."
Los Angeles completed a major upset after finishing eighth in the regular season while the Canucks placed first in the Western Conference and overall for the second season in a row.
"To be honest, it doesn't matter if you lose the seventh game of the finals or you lose in five in the first round, it's devastating," said Daniel Sedin. "We have the mind set to win every year. When you end up on the losing side it's tough."
Brad Richardson also scored for the Kings, who trailed 1-0 after 40 minutes. Richardson tied it up 3:21 into the third period. Goalie Jonathan Quick made 26 saves to earn the win.
"To close out this series, for me personally, and a few guys in the room, it's something we've never done, so it's a great feeling," said Quick.
Henrik Sedin scored the lone Canucks goal, while Schneider stopped 35 shots.
"If you play the way we did in the last three every game you'll be in every game and then our skill is going to take over," said Henrik Sedin.
"In the first game we took way too many penalties. In the second the power play cost us the game. If you do that in a seven-game series, you give away two games, you've got to win four out of five and that's tough when they don't give you an inch out there."
Vancouver's new second line of Ryan Kesler, Alex Burrows and Max Lapierre made a quick impression. Burrows fed Kesler from behind the net about a minute and a half in, but Quick stopped the centre's shot from the slot.
But the Canucks ran into some early penalty trouble and did not get another shot for another six minutes before Lapierre put one on Quick.
Vancouver killed penalties to Dan Hamhuis and Henrik Sedin, but could not get its power play going on its first man advantage.
However, with Henrik Sedin double-shifting, the Canucks capitalized on the second as the Canucks captain put in a cross-ice pass from his twin brother Daniel at 14:04.
The opportunity came after Hamhuis kept a Mike Richards clearing attempt in at the blue-line.
Schneider, starting his third straight game in place of Roberto Luongo, preserved the 1-0 lead as he stopped L.A.'s Anze Kopitar on a breakaway in the dying seconds of the first period. Kopitar put the rebound off the post as time expired.
Both goaltenders stole the show in the second period as neither team could score.
In the early going, Schneider stopped Kopitar's first shot and Dustin Brown on the rebound as the Kings outshot the Canucks 6-0 in the first 4:11.
Later, Schneider robbed Mike Richards on a rebound, snaring the puck with his catching glove. With just over two minutes left in the second, Quick stymied Daniel Sedin on a breakaway, lowering his right pad to block a snapshot. Sedin slammed his stick against the glass in frustration as he went to the bench.
Richardson drew the Kings even 3:21 into the third period as he tapped in a pass from Drew Doughty. The Kings defenceman deked and circled around Canucks defender Keith Ballard and then passed the puck back to Richardson from the end line.
It was the first goal of the series for Richardson, who missed the first three games while recovering from an emergency appendectomy.
"You've got to give credit to the Kings," said Vigneault. "They played a real great series, a real tough opponent, played strong hockey, made the strong plays on the ice and, at the end of the day, they deserved to win."
Notes: The Canucks made just one lineup change, inserting winger Dale Weise in place of Zack Kassian, who was the principal acquisition in the trade that sent Cody Hodgson to Buffalo at the Feb. 27 deadline. ... The Kings did not make any lineup changes from Game 4. ... Vancouver defenceman Sami Salo played his 100th career playoff game.
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