It was Kuemper's third shutout of the season and his 39th in the NHL.
Trevor Moore and Quinton Byfield each had a goal and assist for the Kings (29-25-18), who have points in four of their past five games (1-1-3). Mikey Anderson had two assists.
Lankinen made 34 saves for the Canucks (21-42-8), who have lost the final four games of an eight-game homestand (2-6-0) and 14 of their past 17 (3-11-3).
Vancouver was already eliminated from playoff contention on Sunday.
Scott Laughton gave the Kings a 1-0 lead while on the power play at 17:34 of the first period. Byfield's wrist shot from the top of the right face-off circle caught a piece of Laughton as he set up a screen in front of Lankinen for his first goal in nine games.
Moore made it 2-0 at 1:21 of the second period. Anderson's wrist shot from the left point was tipped by Byfield in the left circle and then deflected off the stick of Moore at the top of the crease and popped over Lankinen into the net.
Artemi Panarin pushed the lead to 3-0 at 19:21 with a backhander from the left circle after Adrian Kempe forced Vancouver forward Jake DeBrusk to turn the puck over in the neutral zone. Panarin picked up the loose puck, skated into the left circle and beat Lankinen to the blocker side.
The Kings outshot the Canucks 32-12 over the first two periods.
Byfield scored an empty-net goal at 17:36 to secure the 4-0 final.
