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 (1-1-3). Mikey Anderson had two assists.
Los Angeles is one point behind the Nashville Predators for the second wild card into the Stanley Cup Playoffs from the Western Conference.
“We were responsible start from finish and huge win for us,” Kuemper said. “[Shutouts] are always fun, but it takes a whole team to get one, so it's just a credit to how well we played and how focused we were tonight.”
Kevin Lankinen made 34 saves for the last-place Canucks (21-42-8), who have lost four straight to end 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.
“It’s hard on everybody right now and it's not easy, but we have to learn from this,” Canucks defenseman Filip Hronek said. “No one else is going to help us. We have to keep grinding. … We have to be better everywhere. We have to win more edge battles, like on the face-offs, we have to win more battles in the D-zone, we have to execute the plays. Everything.”
Kuemper made his best save off Teddy Blueger on a rebound in the slot midway through the first period top keep it scoreless.
“Huge save by him,” Kings interim coach D.J. Smith said. “And that's what changes momentum in this League. If you give that up, then you're trailing and you're a little more stressed.”
Smith talked Wednesday about winning more battles in front of the opposition net to create offense and his team responded by scoring the first two goals on deflections.