Jake DeBrusk won it with his second goal of the game at 2:58 of overtime for Vancouver. He choked up on his stick to convert a backdoor pass at the right post from center Elias Pettersson, who had two assists.
Quinton Byfield and Alex Laferriere each had a goal and an assist for the Kings (35-26-20), who had won five in a row but are 6-0-2 in the month of April. Adrian Kempe also scored, and Darcy Kuemper made 21 saves.
Los Angeles moved into a tie in points (90) for third in the Pacific with the Anaheim Ducks, who lost 3-2 at the Minnesota Wild on Tuesday. The Ducks own the regulation wins tiebreaker with the Kings (25-22).
Kevin Lankinen made 31 saves for the last-place Canucks (25-48-8), who have won three in a row for the third time all season, and the first since winning four in a row from Dec. 14-20.
Defenseman Elias Pettersson put the Canucks ahead 1-0 at 9:21 of the first period with a shot from the top of the left circle that went under the blocker of a screened Kuemper.
Byfield tied it 1-1 at 17:15. He got behind Canucks forward Brock Boeser on a 2-on-2 rush and redirected a cross-ice pass from Laferriere past the extended right pad of Lankinen.
Byfield has scored in five straight road games (seven goals).
DeBrusk scored a power-play goal from the edge of the crease 52 seconds into the second period to put Vancouver back in front 2-1.
Kempe responded just 12 seconds later to tie it 2-2. The Kings cycled the puck behind the net up to Anze Kopitar at the left face-off dot, from where he spotted Kempe alone at the right post for a backdoor tap-in.
Laferriere put Los Angeles ahead 3-2 at 2:17. His initial redirection of Drew Doughty's point shot was stopped by Lankinen, but Laferriere collected his own rebound and slid a backhand past the right pad of the goaltender.
Zeev Buium tied it 3-3 at 9:20 of the second on a pretty give-and-go play. He sent a feed down low to Nils Hoglander from the top of the right circle, skated down into the low slot, and buried the return pass into an open net.
It was his first goal since Jan. 23 (25 games).
