Burrows came up with the game-winner while teammate Mattias Ohlund was in the penalty box for a restraining minor. Burrows got a loose puck in the neutral zone and skated in on Ward, deking him out with a forward feint before going to his backhand shot.
The Hurricanes pulled Ward for a sixth attacker but couldn't come up with the tying goal.
Ryan Kesler scored a goal and two assists for the Canucks, who had dropped eight straight. Mats Sundin and Kevin Bieksa also scored for Vancouver.
Canucks goalie Roberto Luongo made 24 saves to earn the win.
Eric Staal, Joe Corvo and Joni Pitkanen each scored for the Hurricanes, who had won four of their previous five games. Ray Whitney recorded two assists.
Ward gave up the four goals on 24 shots .