Burrows' shootout winner gave Vancouver a 4-3 victory and ended Detroit's 23-game home winning streak.
The Red Wings almost made it 24, but Daniel Sedin scored with 15.4 seconds left in regulation to send the game into overtime.
Recent acquisition Kyle Quincey scored late for the Red Wings to give Detroit a 2-1 lead. Todd Bertuzzi, who just signed two-year contract extension with Detroit, was denied in the shootout before Burrows ended the game and handed the Red Wings their first home loss since Nov. 3 against the Calgary Flames.
The good news for Detroit is that it still earned a point, which is the difference between the two teams in the Western Conference standings. The Canucks and Red Wings do not play again this season, but their paths could cross again in the Western Conference playoffs.