The teams were tied at 2-2 after two periods when Dustin Penner took a pass that bounced off the skate of Jeff Carter and left him open for the game-winning tip-in late in the third.
"I'll give it the benefit of the doubt, Penner said of Carter's involvement in the pass from Mike Richards. "I hope he didn't hurt himself. I was more surprised it went in."
Dustin Brown added an insurance marker in the final seconds to help the Kings draw first blood against the defending Western Conference champions on their home ice.
Los Angeles capitalised on eight powerplay opportunities to put the Canucks on their heels and earn a surprising result.
"They kept us in our end and it's tough, mentally," Vancouver captain Henrik Sedin said.
In the day's other Western Conference series opener in Nashville, Gabriel Bourque scored twice on his post-season debut as the Predators overcame Detroit's rich play-off tradition to forge a 3-2 win over the Red Wings.
Detroit is playing its 21st consecutive post-season, a longer span than the Predators have existed, but Nashville met the challenge to move ahead 1-0 in the series.
Pekka Rinne had 35 saves for the Predators and defenseman Shea Weber drew a roughing penalty at the buzzer for a series of hits on Henrik Zetterberg.
"It's play-offs," Weber said. “He hit me from behind, so we'll see (if there is further discipline form the NHL)."
Over in the Eastern Conference, the Philadelphia Flyers dealt Pittsburgh a body blow in the opening game of their series, fighting back from a three-goal deficit to win 4-3 in overtime.
After going 3-0 down to the Penguins in the first period, Danny Briere started Philadelphia's revival with a goal in the second and another midway through the third before Brayden Schenn tied the score at 3-3 to force overtime.
Jakub Voracek then scored the game-winning goal early in the extra period to give the Flyers the road victory in the opener of their best-of-seven set.
The home team came out strongly on Wednesday and took a 3-0 lead on goals from Sidney Crosby, Tyler Kennedy and Pascal Dupuis but fizzled in the end.