Darcy Rota's seventh goal this season, at 9:03 of the third period, gave host Vancouver its tie with Detroit.
With goalie Greg Stefan sprawled on the ice, Rota slid the puck into an open net after several Canucks had swung unsuccessfully at the puck.
Greg Smith put Detroit ahead at 3:31 of the first period when he beat goalie Richard Brodeur, then Vancouver tied at 8:12 as Ivan Hlinka picked up a loose puck at the side of the net and tucked it behind Stefan.
Less than two minutes later, veteran center Walt McKechnie scored shorthanded and Detroit held a 2-1 lead at the end of the first period.
With back-up goalie Ken Ellacott having replaced Brodeur, the Red Wings increased their lead to 3-1 at 5:12 of the second period when Mike Blaisdell put a rebound high into the Vancouver net.
The Canucks tied with goals 62 seconds apart. Lars Molin scored at 5:29 and Thomas Gradin at 6:31 while Detroit was playing two men short.
But five minutes later, Derek Smith gave the Red Wings a 4-3 lead when he was left alone in front of the Canucks' net and beat the sprawling Ellacott.