Burrows scored two goals while Daniel Sedin had a goal and three assists and Henrik Sedin added four helpers. The Sedins' offensive eruption came after they had both gone three games without a point.
It was Vancouver's 10th straight win over Toronto, covering a span of more than eight years.
Manny Malhotra, Sami Salo and Kevin Bieksa also scored for the Canucks (37-15-6), who posted their sixth win in seven games. Dion Phaneuf
and Nikolai Kulemin
, with 19.2 seconds left in the game, replied for the Maple Leafs (29-24-6), who suffered their sixth loss in seven outings.
The Canucks led 2-0 after a first period in which they outshot the Maple Leafs 11-4.
Burrows opened the scoring 7:49 into the game on a 2-on-1 with Daniel Sedin against Phaneuf. Burrows gave a lead pass to Sedin who delivered a nice flip pass over the Toronto captain's stick and past Toronto goalie James Reimer
Malhotra gave the Canucks a 2-0 lead a minute and 27 seconds later as he dove to tip in Max Lapierre's pass from the side boards. It was only Malhotra's second goal and third point in 14 games.
The Caucks came close to increasing their lead with just under two minutes remaining in the first, but Reimer robbed Henrik Sedin as he tried to put in a rebound from the edge of the crease.
Burrows put the Canucks ahead 3-0 at 3:18 of the second period when he took a pass from Henrik Sedin and wristed home a shot while left alone in the slot.
But Phaneuf put Toronto on the scoreboard just under three minutes later as he one-timed a Phil Kessel
cross-ice pass behind Roberto Luongo.
Moments later, the Canucks goaltender made a diving blocker save on Joffrey Lupul
to maintain Vancouver's two-goal advantage.
Then Luongo foiled Kessl on a rebound during a Toronto power play, gloving the puck after the Leaf fanned on the shot. Kessel slammed his stick against the boards in frustration.
Luongo finished the game with 24 saves on 26 shots.
Daniel Sedin put the Canucks ahead 4-1 midway through the second period when he scored on a pass from the corner boards by Henrik.
That chased Reimer and brought in Jonas Gustavsson
in the Toronto net. Reimer allowed four goals in 18 shots.
Gustavsson let in the first shot he faced. Salo one-timed a Daniel Sedin shot past the screened netminder while on the power play.
Henrik Sedin picked up his fourth assist of the night at 9:09 of the third period as Jannik Hansen re-directed his pass to Bieksa
Vancouver converted one of two power-play opportunities. Toronto was blanked on two. Notes:
Canucks centre Cody Hodgson, a Toronto native, celebrated his 22nd birthday Saturday. ... Canucks D Keith Ballard missed his fifth straight game with a neck injury that is also being investigated for a concussion. ... Leafs D Luke Schenn
returned to the lineup after being a healthy scratch during Wednesday's overtime win in Edmonton. He assisted on Kulemin's late goal. As a result of Schenn's return, rearguard Mike Komisarek
went back to the press box after playing in Edmonton and Calgary. ... Injured Toronto D Carl Gunnarsson
(ankle) has resumed skating on his own. ... Late in the game, a fan threw a dead salmon on the ice.