The Kings (22-11-2) posted their second consecutive victory, while the Canucks (14-15-9) saw a brief winning spell end at two games. The Canucks have yet to win three games in a row this season.
Quick, who now has two shutouts this season, was rarely tested as the Kings outshot the Canucks 38-27 while leading 1-0 after the first period and 3-0 after the second.
Vancouver was shut out for the fourth time in its past 11 games.
Canucks goaltender Jacob Markstrom posted 33 saves as he made his third straight start in place of injured No. 1 netminder Ryan Miller, who is sidelined with an undisclosed lower-body injury.
The game got off to a feisty start as Vancouver defenceman Alex Biega tussled with Kings rearguard Brayden McNabb just 31 seconds in after McNabb blindsided Vancouver captain Henrik Sedin while he had his head down.
About five minutes later, Vancouver rookie defenceman Andrey Pedan fought Jordan Nolan, with the Canuck scoring a clear victory in his first NHL bout. Less than a minute later, Vancouver's Brandon Prust fought McNabb in an apparent attempt to avenge he hit on Sedin.
But the Canucks showed little aggression in the offensive zone most of the night.
Toffoli opened the scoring at 15:33 of the first period after a Milan Lucic pass from the corner bounced off Kopitar to him in the slot. The Kings outshot the Canucks 16-9 in the first after holding an 11-2 edge at one point.
Forbort gave the Kings a 2-0 lead at 1:57 of the second when his long slapshot deflected in off Pedan. McNabb put Los Angeles ahead 3-0 on another slap shot 10 minutes later as Kopitar won a face-off and the puck went back to the blue line.
Toffoli scored his second goal at 5:55 of the third after he stole the puck while the Canucks were trying to come out of their zone and the disk eventually came back to him. He completed his hat-trick by deflecting in Drew Doughty's point shot during a power play at 12:56.
The Canucks will host Anaheim on New Year's Day. The Kings visit the Edmonton Oilers on Tuesday in the second game of a back-to-back set.
NOTES: The Canucks lost winger Sven Baertschi in the second period to an undisclosed lower-body injury. ... Canucks winger Chris Higgins played in his 700th NHL regular-season game. He returned to the lineup after missing two games with a back injury. Meanwhile, Canucks winger Alex Burrows also returned after missing Saturday's win over Edmonton due to a stiff neck. ... In addition to Miller, Vancouver played without injured defencemen Dan Hamhuis (facial fractures), Luca Sbisa (hand) and Chris Tanev (foot) centre Brandon Sutter (sports hernia) and goaltender Ryan Miller (lower body). ...The Kings were missing top scorer Jeff Carter (upper-body), defenceman Matt Greene (shoulder) and wingers Dwight King (foot) and Kyle Clifford (lower-body). Defenceman Christian Ehrhoff was a healthy scratch for the second straight game.